Question

In triangle pqr base qr is divided at x such that qx=1/2xr. If area of triangle pqr=81cm^2, find area of triangle pqx.

Answer 1

here height for both traingle are same .
let height is H
we know,
area of traingle =1/2 height x base

now,
ar (pqr) =1/2 height x base
81 =1/2 H x pq --------(1)

ar (pqx) = 1/2 H (xq)----------(2)
divided equation (1) to (2)
81/ar (pqx)=1/2H (pq)/1/2H (xq)=pq/xq---------(3)

but we have given ,
qx=xr/2
qx+xr=pq
qx+2qx=pq
3qx=pq
pq/qx=3 ---------(4)
put equation (4) in(3)
81/ar (pqx)=3
ar (pqx)=27 cm^2