Question

if the area of two similar triangles are 64cm2 and 121cm2. A side of a bigger triangle is 15.4cm find the length of the corresponding side in the smaller triangle​

Answer 1

Answer :

The length of the corresponding side in smaller triangle is 11.2cm

Given :

• The area of two similar triangles are 64cm² and 121cm²
• A side of bigger triangle is 15.4cm

To Find :

• The length of the side corresponding in the similar smaller triangle.

Theorem to be used :

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

i.e. if ∆ABC ~ ∆PQR then

$\sf \dashrightarrow \dfrac{ar(ABC)}{ar(PQR)} =(\dfrac{AB}{PQ})^{2} = (\dfrac{BC}{QR})^{2}= (\dfrac{CA}{RP})^{2}$

Solution :

Let us consider the side corresponding to the given side be x cm

By theorem :

$\sf \implies \dfrac{64}{121}=(\dfrac{x}{15.4} )^{2}\\\\ \sf \implies \dfrac{x }{15.4}= \dfrac{8}{11} \\\\ \sf \implies x = \dfrac{8\times 15.4}{11} \\\\ \sf \implies x = \dfrac{56}{5} \\\\ \sf \implies x = 11.2$

Thus the length of required corresponding side 11.2cm