Question

the areas of two similar triangle are in the ratio 25sq and 121sq cm find the ratio of their corresponding sides?
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Answer 1

Area of ∆ ABC / Area of ∆ PQR

= (AB / PQ)²

Therefore

25 / 121 = (AB / PQ)²

(5 / 11)² = (AB / PQ)²

AB / PQ = 5 / 11

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Answer 2

Answer:

Ratio of their corresponding sides are   $\frac{5}{11}$

Step-by-step explanation:

Given: Area of 2 similar triangles = 25 cm² and 121 cm²

To find: Ratio of their corresponding sides.

We use Result of Similar triangles which states that If two triangles are similar than the ratio of their area is equal to square of the their corresponding sides.

Let say Δ ABC and ΔXYZ are similar with following sides,

$\frac{AB}{XY}=\frac{CB}{ZY}=\frac{AC}{XZ}$

and ar ΔABC = 25 cm² , ΔXYZ = 121 cm²

So, by using above mentioned result we get,

$\frac{ar\Delta ABC}{ar\Delta XYZ}=\frac{AB^2}{XY^2}=\frac{CB^2}{ZY^2}=\frac{AC^2}{XZ^2}$

$\implies\frac{ar\Delta ABC}{ar\Delta XYZ}=\frac{AB^2}{XY^2}$

$\frac{ar\Delta ABC}{ar\Delta XYZ}=(\frac{AB}{XY})^2$

$\frac{25}{121}=(\frac{AB}{XY})^2$

$\frac{AB}{XY}=\sqrt{\frac{25}{121}}$

$\frac{AB}{XY}=\frac{5}{11}$

Therefore, Ratio of their corresponding sides are   $\frac{5}{11}$