Question

*ΔLMN ~ ΔPQR and 9 x A (ΔPQR ) = 16 x A (ΔLMN). Then find LM : PQ* 1️⃣ 9:16 2️⃣ 16:9 3️⃣ 3:4 4️⃣ 4:3​

Answer 1

Given:

ΔLMN ~ ΔPQR and 9 x A (ΔPQR ) = 16 x A (ΔLMN). Then find LM : PQ.

To find:

LM : PQ

Solution:

9 × A(Δ PQR ) = 16 × A(ΔLMN) . . . [given]

$\implies \frac{A (\triangle LMN)}{A (\triangle PQR )} = \frac{9}{16}$ . . . . (1)

We know that → The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Here we have → Δ LMN ~ Δ PQR, so based on the above theorem, we get

$\frac{A (\triangle LMN)}{A (\triangle PQR )} = [\frac{LM}{PQ}]^2$

from (1), we get

$\implies \frac{9}{16} = [\frac{LM}{PQ}]^2$

taking square roots on both sides

$\implies \sqrt{\frac{3^2}{4^2} } = \sqrt{[\frac{LM}{PQ}]^2}$

$\implies \frac{3}{4} = \frac{LM}{PQ}$

$\implies \bold{LM : PQ= 3:4 }$ → option (3)

Thus, $\boxed{\bold{LM : PQ= 3:4 }}$.

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Also View:

Proof of the theorem: ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

brainly.in/question/2605465

If the ratio of the areas of two similar triangles is 16: 81 Find the ratio of corresponding side.

brainly.in/question/8468854