Question

PQR is a right-angled triangle with the right angle at Q and k being the length of the perpendicular from Q on PR. If l, m and n are the lengths of sides PQ, QR, and PR respectively, then which of the following holds true?

Answer 1

Given : PQR is a right-angled triangle with the right angle at Q and k being the length of the perpendicular from Q on PR.   l, m and n are the lengths of sides PQ, QR, and PR respectively,

To Find : show that lm = nk

Solution:

PQR is a right-angled triangle with the right angle at Q

Area of Δ PQR  = (1/2) * PQ * QR

PQ = l    

QR = m

Area of Δ PQR  = (1/2)lm

perpendicular from Q on PR is k

Area of Δ PQR  =  (1/2) * PR * k

PR   = n

=> Area of Δ PQR  =  (1/2)nk

(1/2)lm = (1/2)nk

=> lm =  nk

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