# NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.4

### Ex 6.4 Class 10 Maths Question 1.

Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.

### Ex 6.4 Class 10 Maths 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.

### Ex 6.4 Class 10 Maths 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:

### Ex 6.4 Class 10 Maths Question 4.

If the areas of two similar triangles are equal, prove that they are congruent.

### Ex 6.4 Class 10 Maths 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.

### Ex 6.4 Class 10 Maths 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.

### Ex 6.4 Class 10 Maths 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.

### Ex 6.4 Class 10 Maths Question 8.

Tick the correct answer and justify
(i) 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 for Ex 6.4 Class 10 Maths Question 8 (i)

(ii) 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