Question

ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate:
(i) The area of ΔABC,
(ii) The length of the perpendicular from A to BC.

Answer 1

(i) Area of the triangle is given by

A = `1/2 xx "AB" xx "AC"`

   = `1/2 xx 4 xx 4`

    = 8 sq .cm

Given the area as 8 sq. cm and using Pythagoras' theorem,

`BC=sqrt(AB^2+AC^2)`

`BC = sqrt(4^2+4^2) = sqrt(32)`

`BC = 4sqrt(2)`

(ii) Again area of the triangle

`A = 1/2 xx "BC" xx h`

`8 = 1/2 xx 4sqrt(2) xx h`  

`8 = 2sqrt(2) xx h`

`h = 8/(2sqrt(2))xxsqrt(2)/sqrt(2)`

`h = (8sqrt(2))/4` 

`h = 2sqrt(2)` cm

h = 2.83 cm