Question

∆ ABC ~ ∆ PQR. A(∆ ABC) : A(∆ PQR) =81:49, write the ratio AC: PR.​

Answer 1

The ratio AC: PR is 9:7.

Step-by-step explanation:

Given information: ∆ ABC ~ ∆ PQR. A(∆ ABC) : A(∆ PQR) =81:49

If two triangles are similar, then the square of the ratio of their corresponding sides is proportional to the ratio of the area of both triangles.

$\dfrac{A(\triangle ABC)}{A(\triangle PQR)}=\dfrac{AC^2}{PR^2}$

$\dfrac{81}{49}=(\dfrac{AC}{PR})^2$

Taking square root on both sides.

$\sqrt{\dfrac{81}{49}}=\dfrac{AC}{PR}$

$\dfrac{9}{7}=\dfrac{AC}{PR}$

Therefore, the ratio AC: PR is 9:7.

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