Question

In the given figure, triangle ABC is right-angled 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

Answer 1

We have right angled at B.

It is given that and

D and E are the mid-points of sides AB and AC respectively.

(i) We need to calculate length of BC.

In right angled at B:

By Pythagoras theorem,

Hence the length of BC is .

(ii) We need to calculate area of .

In right angled at B, D and E are the mid-points of AB and AC respectively.

Theorem states, the line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.

Therefore, .

Thus, (Corresponding angles of parallel lines are equal)

And

area of

D is the mid-point of side AB .

Therefore, area of

Hence the area of is .