## Chapter 6 Triangles Ex 6.4

**Question 1.** **Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm ^{2} and 121 cm^{2}. 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:**

**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:**

**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:**

**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:**

**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:**

**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:** **Justification:** Areas of two similar triangles are in the ratio of the squares of their corresponding sides.