CBSE Class 10 Triangles Sure Shot Questions Set E

Question. Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the length of shadow of smaller pole is 12 m, then length of shadow of bigger pole.
(a) 22 m
(b) 14 m
(c) 13 m
(d) 11 m
Answer: (a) 22 m

Question. It is given that, \( \Delta ABC \sim \Delta EDF \) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm then the sum of the remaining sides of the triangles is
(a) 23.05 cm
(b) 16.8 cm
(c) 6.25 cm
(d) 24 cm
Answer: (a) 23.05 cm

Question. The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is .
(a) 5.4 cm
(b) 6.8 cm
(c) 2.5 cm
(d) 4 cm
Answer: (a) 5.4 cm

Question. If \( \Delta ABC \sim \Delta EDF \) and \( \Delta ABC \) is not similar to \( \Delta DEF \), then which of the following is not true?
(a) \( BC \times EF = AC \times FD \)
(b) \( AB \times EF = AC \times DE \)
(c) \( BC \times DE = AB \times EF \)
(d) \( BC \times DE = AB \times FD \)
Answer: (c) \( BC \times DE = AB \times EF \)

Question. D and E are respectively the points on sides AB and AC of triangle ABC such that AB=3cm, BD = 1.5cm, BC = 7.5cm and \( DE \parallel BC \). Then length of DE is
(a) 2cm
(b) 2.5 cm
(c) 3.75 cm
(d) 3cm
Answer: (c) 3.75 cm

Question. If \( \Delta ABC \) and \( \Delta DEF \) are similar triangles such that \( \angle A = 57^\circ \) and \( \angle E = 83^\circ \). Find \( \angle C \).
(a) \( 33^\circ \)
(b) \( 30^\circ \)
(c) \( 40^\circ \)
(d) \( 83^\circ \)
Answer: (c) \( 40^\circ \)

Question. D and E are points on the sides AB and AC respectively of a \( \Delta ABC \) such that \( DE \parallel BC \). Find the value of x when AD = x cm, DB = (x − 2) cm, AE = (x + 2) cm and EC = (x − 1) cm.
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) None of the options
Answer: (c) 4 cm

Question. In the adjoining figure, ABCD is a trapezium in which \( CD \parallel AB \) and its diagonals intersect at O. If AO = (2x + 1) cm, OC = (5x – 7) cm, DO = (7x − 5) cm and OB = (7x + 1) cm, find the value of x.
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) None of the options
Answer: (a) 2 cm

Question. \( \Delta ABC \) is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If \( \Delta DEF \sim \Delta ABC \) and FE = 4 cm, then find the perimeter of \( \Delta DEF \).
(a) 12 cm
(b) 13 cm
(c) 14 cm
(d) 15 cm
Answer: (d) 15 cm

Question. A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.
(a) 12 m
(b) 10 m
(c) 9 m
(d) 11 m
Answer: (c) 9 m

Question. A 15 metres high tower casts a shadow 24 meters long at a certain time and at the same time, a telephone pole casts a shadow 16 meters long. Find the height of the telephone pole.
(a) 12 m
(b) 10 m
(c) 9 m
(d) 11 m
Answer: (b) 10 m

Question. ABCD is a trapezium in which \( AB \parallel DC \) and P and Q are points on AD and BC, respectively such that \( PQ \parallel DC \). If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.
(a) 20 cm
(b) 40 cm
(c) 60 cm
(d) 80 cm
Answer: (c) 60 cm

Question. If \( \Delta ABC \sim \Delta DEF \), AB = 4 cm, DE = 6 cm. EF = 9 cm and FD = 12 cm, find the perimeter of \( \Delta ABC \).
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm
Answer: (d) 18 cm

Question. The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm. find AB.
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm
Answer: (c) 16 cm

Question. A vertical stick of length 7.5 m casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the tower.
(a) 20 m
(b) 40 m
(c) 60 m
(d) None of the options
Answer: (d) None of the options

Question. Assertion: A line drawn parallel to any one side of a triangle intersects the other two sides proportionally.
Reason: Parallel lines cannot be drawn to any one side of a triangle.
(a) Both A and R are true and R is the correct reason of A.
(b) Both A and R are true and R is not the correct reason of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer: (c) A is true but R is false.

Question. E and F are the points on the sides PQ and PR respectively of a triangle PQR. PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm.
Assertion: EF is not parallel to QR
Reason: In a triangle if two sides are divided proportionally by a line then the line is parallel to the third side.
(a) Both A and R are true and R is the correct reason of A.
(b) Both A and R are true and R is not the correct reason of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer: (d) A is false but R is true.

Question. Assertion: If two angles of any triangle are equal to the corresponding two angles of another triangle then the third angles are not necessarily equal.
Reason: The sum of three angles of any triangle is equal to 180°
(a) Both A and R are true and R is the correct reason of A.
(b) Both A and R are true and R is not the correct reason of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer: (d) A is false but R is true.

Question. Assertion: If any two sides of a triangle are proportional to corresponding two sides of another triangle and the included angles are equal then the triangles are similar by SAS similarity criterion.
Reason: If the equal angles are not included between the proportional sides, then SAS criterion will be void.
(a) Both A and R are true and R is the correct reason of A.
(b) Both A and R are true and R is not the correct reason of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer: (a) Both A and R are true and R is the correct reason of A.