Question

Ratio of corresponding sides of two similar triangles is $2:5$,if the area of the smaller triangle is $64sq$ cm,then what is the area of the bigger triangle?

Answer 1

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 .

Here ,

Let $A_1,A_2$ are areas of two similar

triangles and $s_1,s_2$ are their

corresponding sides respectively ,

$s_1:s_2=2:5$

$=>s_1/s_2=2/5$ -----$\left(1\right)$

$A_1=64m²,$

$A_2=?$

$\left(s_1/s_2\right)²=\left(A_1/A_2\right)$

$=>\left(2/5\right)²=\left(64/A_2\right)$

$=>A_2=(64\times 25)/4$

$=16\times 25$

$=400$

Therefore ,

Area of bigger triangle $\left(A_2\right)=400cm²$