Question

The ratio of the corresponding sides of two similar triangles is 2 : 3. If the area of the smaller triangle is 100 cm², find the area of the larger triangle.​

Answer 1

Answer:

Question

The ratio of the corresponding sides of two similar triangles is 2 : 3. If the area of the smaller triangle is 100 cm², find the area of the larger triangle.

Answer

$\frac{area \: of \: 1st \: triangle}{area \: of \: 2nd \: triangle} = \frac{ {2}^{2} }{ {3}^{2} }$

Let's be the area of larger triangle x

$\frac{ {100}^{2} }{ {x}^{2} } = \frac{ {2}^{2} }{ {3}^{2} }$

$x = \frac{9}{4} \times {100}^{2}$

$x = {225}^{2}$

$\longrightarrow \: hence \: the \: area \: of \: larger \: triangle \: = {225}^{2}$