Question

ΔLMN ~ ΔPQR , 16 x A(ΔPQR) = 9 x A(ΔLMN) , If LM = 20 then PQ = ?

Answer 1

Answer:

PQ=15

Step-by-step explanation:

Given

ΔLMN ~ ΔPQR

LM=20

16×ar(PQR)=9×ar(LMN)

ar(LMN)/ar(PQR)=16/9 (1)

as we know that given triangle are congruent

ar(triangle 1)/ar(triangle 2)=side A of triangle 1/side A of triangle 2

ar(ΔLMN )/ar(ΔPQR)=LM²/PQ²

Substituting values in (1)

LM²/PQ²=16/9

(20)²/PQ²=16/9

400×9/16=PQ²

225=PQ²

PQ=15 units (negative value is ignored as distances are never negative)