Question:

LMN ~ PQR, 9 ×A(PQR ) = 16 ×A(LMN). If QR = 20 then find MN.

Answer:

Given 9 ×A(PQR ) = 16 ×A(LMN)
A(PQR )/ A(LMN) = 16/9…………(i)
LMN ~ PQR
A(PQR )/ A(LMN) = QR^2/MN² …..(ii)
From (i) and (ii)
QR^2/MN² = 16/9
Given QR = 20
20²/MN² = 16/9
Taking square root on both sides
20/MN = 4/3
MN = 20×3/4
MN = 15
Hence the measure of MN is 15 units.

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LMN ~ PQR, 9 ×A(PQR ) = 16 ×A(LMN). If QR = 20 then find MN.

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