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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.
Solution
(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
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