CBSE Class 10 Mathematics Triangles MCQs Set 07

Question. In \(\triangle ABC, DE \parallel BC\) and \(\frac{AD}{DB} = \frac{3}{5}\). What is the length of \(AE\) if \(AC = 4.8\) cm?
(a) 1.4cm
(b) 1.8cm
(c) 2.2 cm
(d) 3.6 cm
Answer: B

Question. In \(\triangle ABC\), if \(\frac{AD}{DB} = \frac{AE}{EC}\) and \(\angle ADE = \angle ACB\), what type of triangle is \(\triangle ABC\)?
(a) Right triangle
(b) Acute angled triangle
(c) Isosceles triangle
(d) Obtuse angled triangle
Answer: C

Question. The altitudes of two similar triangles are 4 cm and 6 cm. If the area of one triangle is \(36 \text{ cm}^{2}\), what is the area of the other?
(a) \(16\text{ cm}^{2}\)
(b) \(36\text{ cm}^{2}\)
(c) \(49\text{ cm}^{2}\)
(d) \(25\text{ cm}^{2}\)
Answer: A

Question. The ratio of areas of two similar triangles is \(81 : 49\). If the median of one triangle is 4.9 cm, what is the median of the other?
(a) 4.9 cm
(b) 6.3 cm
(c) 7 cm
(d) 9 cm
Answer: B

Question. The perimeters of two similar triangles ABC and DEF are 24 cm and 32 cm respectively. If \(DE = 12\) cm, find AB.
(a) 9cm
(b) 35cm
(c) 18cm
(d) 28cm
Answer: A

Question. BC and EF are the corresponding sides of two similar triangles ABC and DEF. If \(BC = 9.1\) cm, \(EF = 6.5\) cm and the perimeter of \(\triangle DEF\) is 35 cm, find the perimeter of \(\triangle ABC\).
(a) 15cm
(b) 49cm
(c) 45 cm
(d) 35 cm
Answer: B

Question. A man cycles 15 m towards east, turns right and cycles 8 m. How far is he from the starting point?
(a) 7m
(b) 17m
(c) 23m
(d) 19m
Answer: B

Question. At what height does the tip of a 34m long ladder placed at a distance of 16 m from a wall, touch the wall?
(a) 29 m
(b) 34 m
(c) 30m
(d) 18 m
Answer: C

Question. At some point of time on a summer evening, an 8 m tall flag post casts a 15 m long shadow. What is the distance between the tips of the flag post and its image?
(a) 15m
(b) 28m
(c) 23m
(d) 17m
Answer: D

Question. What is the area of a square of diagonal 12cm?
(a) \(36\text{ cm}^{2}\)
(b) \(9\text{ cm}^{2}\)
(c) \(72\text{ cm}^{2}\)
(d) \(144\text{ cm}^{2}\)
Answer: C

Question. Two 15 m strings are tied to a peg between two poles 9 m and 12 m long from their tops. What is the distance between the poles?
(a) 18m
(b) 21 m
(c) 20 m
(d) 23 m
Answer: B

Question. The areas of two similar triangles are \(81 \text{ cm}^{2}\) and \(49 \text{ cm}^{2}\) respectively. If the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the smaller triangle.
(a) 3 cm
(b) 2.5 cm
(c) 4 cm
(d) 3.5 cm
Answer: D

Question. In similar triangles \(\triangle ABC\) and \(\triangle FDE\), \(DE = 4\) cm, \(BC = 8\) cm and area of \(\triangle FDE = 25 \text{ cm}^{2}\). What is the area of \(\triangle ABC\)?
(a) \(144\text{ cm}^{2}\)
(b) \(121\text{ cm}^{2}\)
(c) \(100\text{ cm}^{2}\)
(d) \(81\text{ cm}^{2}\)
Answer: C

Question. Given that \(PB \perp AB\) and \(QA \perp AB\), \(PO = 4\) cm and \(QO = 7\) cm, if area of \(\triangle QAO\) is \(245 \text{ cm}^{2}\), what is the area of \(\triangle PBO\)?
(a) \(60\text{ cm}^{2}\)
(b) \(40\text{ cm}^{2}\)
(c) \(125\text{ cm}^{2}\)
(d) \(80\text{ cm}^{2}\)
Answer: D

Question. A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of the girls shadow after 4 seconds.
(a) 4.8m
(b) 1.2m
(c) 1.6m
(d) 3.6m
Answer: C

Question. If \(\triangle ABC \sim \triangle DEF, BC = 3\) cm, \(EF = 4\) cm and area of \(\triangle ABC = 54 \text{ cm}^{2}\), find the area of \(\triangle DEF\).
(a) \(96\text{ m}^{2}\)
(b) \(16\text{ cm}^{2}\)
(c) \(96\text{ cm}^{2}\)
(d) \(69\text{ cm}^{2}\)
Answer: C

Question. In \(\triangle ABC, \angle A = 90^{\circ}, AN \perp BC\), \(BC = 12\) cm and \(AC = 5\) cm. Find the ratio \(ar(\triangle ANC) : ar(\triangle ABC)\).
(a) \(12^{2} : 5^{2}\)
(b) \(3^{2} : 12^{2}\)
(c) \(5^{2} : 12^{2}\)
(d) \(3^{2} : 5^{2}\)
Answer: C

Question. In trapezium ABCD, \(AB \parallel CD\). If \(OA = x - 4, OB = 3x - 19, OC = 4\) and \(OD = x - 3\), find 'x'.
(a) 10 units
(b) 9 units
(c) 12 units
(d) 8 units
Answer: D

Question. In \(\triangle ABC, \angle B > 90^{\circ}\) and \(AD \perp CB\) (produced). Identify the correct statement.
(a) \(AC^{2} = AB^{2} + BC^{2} + 2BC \cdot BD\)
(b) \(AC^{2} = AB^{2} + BC^{2} + 2BC \cdot AB\)
(c) \(AB^{2} = AC^{2} - BC^{2} + 2BC \cdot BD\)
(d) \(AC^{2} = AB^{2} + BC^{2} - 2BC \cdot BD\)
Answer: A

Question. Two triangles BAC and BDC, right angled at A and D respectively, are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, which of the following statements is true?
(a) \(AP \times PC = DP \times PB\)
(b) \(\frac{AP}{PC} = \frac{DP}{PB}\)
(c) \(AP \times PB = DP \times PC\)
(d) Both (b) and (c)
Answer: A

Question. In \(\triangle ABC\), D is a point on AB and E is a point on BC such that \(DE \parallel AC\) and area of \(\triangle DBE = \frac{1}{2}\) area of \(\triangle ABC\). Find \(\frac{AD}{AB}\).
(a) \(\frac{1 - \sqrt{2}}{2}\)
(b) \(\frac{\sqrt{2} - 1}{\sqrt{2}}\)
(c) \(\frac{\sqrt{2} - 1}{2}\)
(d) \(\frac{\sqrt{2} + 1}{2}\)
Answer: B

Question. In \(\triangle ABC, \angle A = 90^{\circ}\) and \(AD \perp BC\). If \(AB = 5\) cm, \(BC = a\) cm and \(AC = b\) cm, find the length of BD in cm.
(a) \(\frac{b^{2} - a^{2} + 25}{a}\)
(b) \(\frac{a^{2} - b^{2} + 25}{2a}\)
(c) \(\frac{a^{2} - b^{2} + 25}{2b}\)
(d) \(\frac{a^{2} + b^{2} + 25}{2a}\)
Answer: B

Question. If \(\triangle ABC\) is an equilateral triangle of side 'a' and D is a point on BC such that \(BD = \frac{1}{3}BC\), what is the length of AD?
(a) \(\sqrt{\frac{7}{3}}a\)
(b) \(\frac{3}{\sqrt{7}}a^{2}\)
(c) \(\frac{\sqrt{7}}{3}a\)
(d) \(\frac{\sqrt{7}}{3}a^{2}\)
Answer: C

Question. \(\triangle ABC\) is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of \(\triangle ABC\) and \(\triangle ACD\).
(a) \(1 : 2\)
(b) \(3 : 1\)
(c) \(1 : 3\)
(d) \(4 : 1\)
Answer: A

Question. If \(\triangle ABC \sim \triangle DFE, \angle A = 30^{\circ}, \angle C = 50^{\circ}, AB = 5\) cm, \(AC = 8\) cm and \(DF = 7.5\) cm. Which of the following is true?
(a) \(DE = 12\) cm, \(\angle F = 50^{\circ}\)
(b) \(DE = 12\) cm, \(\angle F = 100^{\circ}\)
(c) \(EF = 12\) cm, \(\angle D = 100^{\circ}\)
(d) \(EF = 12\) cm, \(\angle D = 30^{\circ}\)
Answer: B

Question. \(\triangle ABC\) is right-angled at C. If p is the length of perpendicular from C to AB and \(AB = c, BC = a\) and \(CA = b\), which of the following is true?
(a) \(pc = ab\)
(b) \(pb = ab\)
(c) \(pc = bc\)
(d) \(pb = ac\)
Answer: A

Question. \(\triangle ABC\) is right angled at C and \(AC = \sqrt{3}BC\). What is the value of \(\angle ABC\)?
(a) \(30^{\circ}\)
(b) \(90^{\circ}\)
(c) \(60^{\circ}\)
(d) \(45^{\circ}\)
Answer: C

Question. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. What is the length of the side of the rhombus?
(a) 9cm
(b) 10cm
(c) 8 cm
(d) 20 cm
Answer: B

Question. If \(\triangle ABC\) and \(\triangle PQR\) are similar and \(\frac{BC}{QR} = \frac{1}{3}\), find \(\frac{ar(\triangle PQR)}{ar(\triangle BCA)}\).
(a) 9
(b) 3
(c) \(\frac{1}{3}\)
(d) \(\frac{1}{9}\)
Answer: A

Question. A man drives 13 km in the north west direction, turns left and drives 5 km. How far is he from the starting point?
(a) 10km
(b) 18km
(c) 12 km
(d) 11 km
Answer: C

Question. What is the ratio of areas of two similar triangles whose corresponding sides are in the ratio \(15:19\)?
(a) \(\sqrt{15} : \sqrt{19}\)
(b) \(15:19\)
(c) \(225:361\)
(d) \(125:144\)
Answer: C

Question. Identify the incorrect statement.
(a) A right angled triangle may have 1, 1 and 2 as its sides.
(b) \(1, 2, \sqrt{3}\) are the sides of a right angled triangle.
(c) The ratio of corresponding sides of two squares whose areas are in the ratio \(4:1\) is \(2 : 1\).
(d) 17, 8 and 15 are the sides of a right angled triangle.
Answer: A

Question. Points P and Q on the sides AB and AC of \(\triangle ABC\) are such that \(PQ \parallel BC\), \(AP:PB = 2 : 3\) and \(AQ = 4\) cm. What is the measure of AC?
(a) 12cm
(b) 16cm
(c) 10cm
(d) 15cm
Answer: C

Question. The side of an equilateral triangle is 10 cm. What is its altitude?
(a) \(5\sqrt{2}\)cm
(b) \(5\sqrt{3}\)cm
(c) 12cm
(d) 5cm
Answer: B

Question. The diagonals of a rhombus are 16 cm and 12 cm. What is the measure of its side?
(a) 10cm
(b) 12cm
(c) 8cm
(d) 16cm
Answer: A