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in Quadrilaterals by (56.3k points)

In figure, triangle ABC is a right-angled triangle at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid-points of the sides AB and AC respectively, calculate 

(i) The length of BC

(ii) The area of ΔADE.

1 Answer

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Best answer

In ΔABC, ∠B = 90° (Given) 

AB = 9 cm, AC = 15 cm (Given) 

By using Pythagoras theorem 

AC2 = AB2 + BC2 

⇒152 = 92 + BC2 

⇒BC2 = 225 – 81 

= 144 

or BC = 12 

Again, 

AD = DB = AB/2 = 9/2 = 4.5 cm [D is the mid−point of AB 

D and E are mid-points of AB and AC 

DE ∥ BC ⇒ DE = BC/2 [By mid−point theorem] 

Now, 

Area of ΔADE = 1/2 x AD x DE

= 1/2 x 4.5 x 6 

= 13.5 

Area of ΔADE is 13.5 cm2

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