CBSE Class 10 Mathematics Triangles MCQs Set 03

Question. If in two triangles ABC and PQR, ∠A= ∠Q and ∠R=∠B , andthen which of the following is not true.
(a) AB/PQ =BC/RP
(b) BC/PR =AC/PQ
(c) BC/RP =AB/QR
(d) AB/QR =AC/PQ

Answer: A

Question. If ΔABC∼PQR such that AB = 9.1 cm and PQ = 6.5 cm. If the perimeter of ΔPQR is 25 cm, then the perimeter of ΔABC is
(a) 34 cm
(b) 35 cm
(c) 36 cm
(d) 30 cm

Answer: B

Question. In ∠ABC , if AD/DB = AE/EC and ∠ADE = ∠ACB , what type of triangle is ΔABC ?
(a) Right triangle
(b) Acute angled triangle
(c) Isosceles triangle
(d) Obtuse angled triangle

Answer: C

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

Answer: B

Question. In an isosceles triangle ABC if AC = BC and AB² = 2AC² then the measure of ∠C is
(a) 90^o
(b) 45^o
(c) 60^o
(d) 30^o

Answer: A

Question. What will be the length of the hypotenuse of an isosceles right triangle whose one side is 4√2cm
(a) 12√2cm
(b) 12 cm.
(c) 8 cm.
(d) 8√2

Answer: C

Question. It is given that ΔABC ∼ ΔDFE , ∠A = 30° , ∠C =40°, AB =5 cm, AC =8cm and DF =7.5 cm Then, the following is true.
(a) ∠F =100° ,DE =12cm
(b) ∠F =40° ,DE =12cm
(c) ∠D =110° ,EF =12cm
(d) ∠D =30° , EF =12cm

Answer: A

Question. The areas of two similar triangles are respectively . If the median of the first triangle is 12.1 cm, then the corresponding median of the other triangle is equal to
(a) 8.1 cm
(b) 8.8 cm
(c) 11 cm
(d) 11.1 cm

Answer: B

Question. In the given figure, ΔABC ∼ ΔDEF, BC = 3 cm, EF = 4 cm and area of ΔABC = 54 cm². Then the area of ΔDEF is   
(a) 54 cm²
(b) 88 cm²
(c) 96 cm²
(d) 108 cm²

Answer: C

Question. If two sides of a right triangle are 9 cm and 12 cm, then its third side will be
(a) 21 cm
(b) 15 cm
(c) 3 cm
(d) None of the options

Answer: B

Question. Out of the given statements
i. The areas of two similar triangles are in the ratio of the corresponding altitudes.
ii. If the areas of two similar triangles are equal, then the triangles are congruent.
iii. The ratio of areas of two similar triangles is equal to the ratio of their corresponding medians.
iv. The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
The correct statement is
(a) (iii)
(b) (ii)
(c) (i)
(d) (iv)

Answer: B

Question. If ΔABC is an equilateral triangle of side ‘a’ and D is a point on BC such that BD = – BC, what is the length of AD?
(a) √7/3 a
(b) 3/√7 a²
(c) √7/3 a
(d) √7/3 a²

Answer: C

Question. If in two triangles ABC and DEF, AB/DE =BC/FE =CA/FD , then
(a) ΔFDE ∼ ΔABC
(b) ΔBCA ∼ ΔFDE
(c) ΔFDE ∼ ΔCAB
(d) ΔCBA ∼ ΔFDE

Answer: C

Question. A semicircle is drawn on A(c) Two chords AB and BC of length 8 cm and 6 cm respectively are drawn in the semicircle. What is the measure of the diameter of the circle?
(a) 10 cm
(b) 12 cm
(c) 11 cm
(d) 14 cm

Answer: A

Question. In an equilateral triangle ABC, D is a point on the side BC such that BD = 1 3 BC. Then 9AD² =   
(a) 7 AB²
(b) 5 AB²
(c) 8 AB²
(d) 11 AB²

Answer: A

Question. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, the length of her shadow after 4 seconds is
(a) 1.1 cm
(b) 1.6 cm
(c) 2.3 cm
(d) 3.5 cm

Answer: B

Question. Given that PB ⊥ AB and QA ⊥ AB PO=4 cm and QO = 7cm , if area of ΔQAO is 245 cm² , what is the area of ΔPBO?
(a) 2 60 cm
(b) 2 40 cm
(c) 2 125 cm
(d) 2 80 cm

Answer: D

Question. In ΔABC,∠A = 90° and AD±BC. If AB= 5 cm, BC = a cm and AC = b cm, find the length of BD in cm.
(a) (b² – a² + 25/ a)
(b) (a² – b² + 25/ 2a)
(c) (a² + b² + 25/ 2b)
(d) (a² – b² + 25/ 2a)

Answer: B

Question. In ΔABC, ∠B> 90° and AD ⊥ CB (produced). Identify the correct statement.
(a) AC² = AB² + BC² + 2BC.AD
(b) AC² = AB² + BC² + 2BC.AB
(c) AB² = AC² + BC² + 2BC.BD
(d) None of the options

Answer: A

Question. If ΔABC ∼ ΔDFE ∠A =30° , ∠C = 50° , AB = 5cm, ∠AC = 8cm and DF = 7.5 cm . Which of the following is true ?
(a) DE = 12cm, ∠F = 50°
(b) DE = 12cm, ∠F =100°
(c) EF = 12cm, ∠D =100°
(d) EF = 12cm, ∠D = 30°

Answer: B

Question. A street light is fixed on a pole 6 m above the groun(d) If a woman of height 1.5 m casts a shadow of 3, then distance between her and the base of the pole is _____.
(a) 12 m
(b) 9 m
(c) 8 m
(d) 10 m

Answer: B

Question. In an equilateral ΔABC AD⊥ BC and AD² =P. BC² , then p is equal to
(a) 1/2
(b) 3/4
(c) 2/3
(d) 1/3

Answer: B

Question. ABCD is a trapezium in which AB || DC and AB = 2D(c) Diagonals AC and BD intersect at O. If ar(ΔAO) = 84 cm², ar (ΔCOD) then is equal to   
(a) 24 cm²
(b) 42 cm²
(c) 28 cm²
(d) 21 cm²

Answer: D

Question. Two poles of height a and b (b > a) are c metres apart. The height h (in metres) of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is
(a) ab
(b) ab + 2ab
(c) ab /a + b
(d) None of the options

Answer: C

Question. Two poles of height 8 m and 13 m are standing 12 m apart. The distance between their tops is _____
(a) 15 m
(b) 17 m
(c) 13 m
(d) 19 m

Answer: C

Assertion and Reason
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : ABC is an isosceles, right triangle, right angled at C. Then AB2 = 3AC².     
Reason : In an isosceles triangle ABC if AC = BC and AB² = 2AC², then ∠C = 90°.

Answer: D

Question. Assertion : ABC and DEF are two similar triangles such that BC = 4 cm, EF = 5 cm and area of ΔABC = 64 cm², then area of ΔDEF = 100 cm².   
Reason : The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.

Answer: B

Question. Assertion : If in a ΔABC, a line DE || BC, intersects AB in D and AC in E, then AB /AD = AC/ AE .
Reason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

Answer: A

One Word Questions :

Question. The perimetres of two similar triangles ABC and PQR are respectively 36cm and 24cm. If PQ = 10cm, find AB.
Answer: 15cm

Question. The lengths of sides of a triangle are 12cm, 16cm and 21cm. The bisector of the greatest angle divides the opposite side into two parts. Find the length of these two parts.
Answer: 9cm, 12cm

Question. AB=5cm, BC = 2cm and AC = √29 cm are the sides of ABC. Then what is the measure of B ?
Answer: 90°

Question. In an equilateral ΔABC of side ‘a’, what is the height of ΔABC ?
Answer: √3/2 a

Question. In a triangle, the internal bisector of angle bisect the opposite side; what type of triangle is this?
Answer: Isosceles

Question. A boy goes 15m due east and 20m due north. How far is he from the starting point?
Answer: 25cm

Question. If ΔABC ∼ ΔDEF , ar(ΔDEF)=100cm² and AB/DE = 1/2 . then find the area of ΔABC .
Answer: 25cm²

Question. A ladder is placed in such a way that its foot is at a distance 5cm from the wall and its top reaches a window 12cm above the ground. Determine the length of the ladder.
Answer: 13cm

Question. Two triangle ABC and DEF are similar. If AB = 10cm and DE = 8cm, find the ratio of the areas of ΔABC and ΔDEF .
Answer: 25/16