Question

Let triangle abc similar to triangle def and their areas be, respectievely 64 cm2 and 121cm2 . If ef = 15.4 cm, find bc.

Answer 1

BC = 11.2 centimeters

Answer 2

Answer:

$BC = 11.2 \:cm$

Step-by-step explanation:

$Given \\\triangle ABC \: and \: \triangle DEF\: are \: similar$

$Area \:of\: \triangle ABC (A_{1})=64\:cm^{2}\\Area \:of\: \triangle DEF (A_{2})=121\:cm^{2}\\and\: EF =15.4 \:cm$

To Find :

BC = ?

/* we know the Theorem :

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.*/

$\frac{BC^{2}}{EF^{2}}=\frac{A_{1}}{A_{2}}$

$\implies \frac{BC^{2}}{(15.4)^{2}}=\frac{64\: cm^{2}}{121\:cm^{2}}$

$\implies \frac{BC^{2}}{(15.4)^{2}}=\frac{(8\: cm)^{2}}{(11\:cm)^{2}}$

$\implies \big(\frac{BC}{15.4}\big)^{2}=\big(\frac{8\: cm}{11\:cm}\big)^{2}$

$\implies \frac{BC}{15.4}=\frac{8}{11}$

$\implies BC = \frac{8\times 15.4}{11}$

$\implies BC = 8 \times 1.4$

$\implies BC = 11.2\:cm$

Therefore,

$BC = 11.2 \:cm$

•••♪