CBSE Class 10 Mathematics Triangles VBQs

Question. In the adjoining figure, ABCD is a trapezium in which CD ∥ 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 above
Answer : A

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

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 these
Answer : D

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

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

Question. If ΔABC ∼ ΔDEF, AB = 4 cm, DE = 6 cm. EF = 9 cm and FD =12 cm, find the perimeter of ΔABC.
(A) 12 cm
(B) 14 cm
(C) 16 cm
(D) 18 cm
Answer : D

Question. In the given figure, if ∠ADE = ∠B, AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm and BC = 4.2 cm, find DE.
(A) 2 cm
(B) 2.5 cm
(C) 2.8 cm
(D) 3 cm
Answer : C

Question. ΔABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ΔDEF ∼ ΔABC and FE = 4 cm, then find the perimeter of ΔDEF.
(A) 12 cm
(B) 13 cm
(C) 14 cm
(D) 15 cm
Answer : D

Question. In the given figure, ∠CAB = 90°, AD ⊥ BC, AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.
(A) 20 cm
(B) 40 cm
(C) 60 cm
(D) 80 cm
Answer : C

Question. ABCD is a trapezium in which 𝐴𝐵∥𝐷𝐶 and P and Q are points on AD and BC, respectively such that 𝑃𝑄∥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

Question. A: Assertion: A line drawn parallel to any one side of a triangle intersects the other two sides proportionally.
R: 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

Question. A: 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.
R: 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

Question. A: 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.
R: 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 : B

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.
A: Assertion: EF is not parallel to QR
R: 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

Question. A man goes 12 m due west and then 9 m due north. How far is he from the starting point?
(a) 12 m
(b) 15 m
(c) 18 m
(d) 24 m
Answer : B

Question. In ΔABC, AB = 6√3 cm , AC = 12 cm and BC = 6 cm, then ∠B =
(a) 30°
(b) 60°
(c) 90°
(d) 45°
Answer : C

Question. In DABC, ∠ABC = 90°. AD and CE are two medians drawn from A and C, respectively. If AC = 5 cm and AD = 3√5/2 cm , the length of CE is
(a) 2√5 cm
(b) 3√5 cm
(c) 4√5 cm
(d) √5 cm
Answer : A

Question. If in ΔABC, AB = 9 cm, BC = 40 cm and AC = 41 cm, then the ΔABC is a/an
(a) Acute angled triangle
(b) Right triangle
(c) Obtuse angled triangle
(d) Isosceles triangle
Answer : B

Question. If in an equilateral triangle, the length of the median is √3 cm, then the length of the side of equilateral triangle is
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm
Answer : B

Question. A ladder is placed against a wall such that its foot is at distance of 5 m from the wall and its top reaches a window 5 3 m above the ground. The length of the ladder is
(a) 10 m
(b) 15 m
(c) 18 m
(d) 24 m
Answer : A

Question. In an equilateal triangle of side 3√3 cm, the length of the altitude is
(a) 3.5 cm
(b) 4 cm
(c) 4.5 cm
(d) 6 cm
Answer : C

Question. In ΔABC, ∠B = 90° and BD ⊥ AC. If AC = 9 cm and AD = 3 cm, then BD is equal to
(a) 2√2 cm
(b) 3√2 cm
(c) 2√3 cm
(d) 3√3 cm
Answer : B

Question. ABC is an isosceles triangle right-angled at C. The AB² is equal to
(a) AC²
(b) 2AC
(c) AC²
(d) AC/²
Answer : C

Question. In an isosceles triangle PQR, PQ = QR and PR² = 2PQ². Then ∠Q is
(a) 30°
(b) 60°
(c) 90°
(d) None of these
Answer : C
 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If two sides of a right angle are 7 cm and 8 cm, then its third side will be 9 cm.
Reason (R): In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides
Answer : D

Question. Assertion (A): In the ∆ABC, AB = 24 cm, BC = 10 cm and AC = 26 cm, then ∆ABC is a right angle triangle.
Reason (R): If in two triangles, their corresponding angles are equal, then the triangles are similar.
Answer : B