Question

ΔLMN~ΔPQR, 9*A (ΔPQR )=16 *A(ΔLMN). If QR = 20 then find MN.

Answer 1

15 will be the answer

Answer 2

Answer:

MN = 15

Step-by-step explanation:

In the given question,

The triangles LMN and PQR are similar.

Also,

9.Area(PQR) = 16.Area(LMN) (Given)

and,

QR = 20 (Given)

So,

In triangles LMN and PQR, using the law of similarity we can say that,

$\frac{ar(LMN)}{ar(PQR)} =\frac{MN^{2}}{QR^{2}}$

Now,

On putting the values from the given we get,

$\frac{ar(LMN)}{ar(PQR)} =\frac{9}{16}=\frac{MN^{2}}{QR^{2}}\\\frac{9}{16}=\frac{MN^{2}}{QR^{2}}\\So,\\\frac{MN}{QR}=\frac{3}{4}\\\frac{MN}{20}=\frac{3}{4}\\So,\\MN=15$

Therefore, the value of MN is given by,

MN = 15