NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

These NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.4

Question 1.
Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC.
Solution:
Since, ∆ABC ~ ∆DEF
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.

Question 2.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Solution:
ABCD is a trapezium with AB || DC and AB = 2 CD

Question 3.
In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that

Solution:

Question 4.
If the areas of two similar triangles are equal, prove that they are congruent.
Solution:
Given : Areas of two similar triangles are equal.
To Prove : Triangles are congruent. Ratio in the areas of two similar triangles is equal to the ratio of their respective sides.
Proof: Let ∆ABC and ∆PQR be two triangles.

Hence, by SSS congruence theorem
∆ ABC ≅ ∆PQR (Proved)

Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.
Solution:
ABC is a triangle and D, E, F are the mid¬points of the sides AB, BC and CA respectively

Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
Given ∆ ABC ~ ∆DEF, and AP and DQ are their medians.

Question 7.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Solution:
Given A square ABCD. Equilateral ABCE and AACF have been described on side BC diagonal AC respectively.

Question 8.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is _________.
(a) 2 : 1
(b) 1 : 2
(c) 4 : 1
(d) 1 : 4
Solution:
(c) 4 : 1

Question 9.
Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio __________.
(a) 2 : 3
(b) 4 : 9
(c) 81 : 16
(d) 16 : 81
Solution:
(d) 16 : 81