Q13 of 186 Page 229

In ΔABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

In ΔABC and ΔADE

It is given that AD = DB and AE = EC

Also ∠ A = ∠ A

So, by SAS similarity criterion ΔADE ~ ΔABC

We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

ΔABC is right-angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm, find the ratio of the areas of ΔABC and ΔADC.

In the given figure and DE : BC = 3: 5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.

The sides of certain triangles are given below. Determine which of them are right triangles.

(i) 9 cm, 16 cm, 18 cm

(ii) 7 cm, 27 cm, 25 cm

(iii) 1.4 cm, 4.8 cm, 5 cm

(iv) 1.6 cm, 3.8 cm, 4 cm

(v) (a - 1) cm, 2 √a cm, (a + 1) cm

A man goes 80 m due east and then 150 m due north. How far is he from the starting point?