Question

The perimeter of two similar triangles are 12cm and 72cm.If the area of smaller triangle is 6cm sqare. Find the area of bigger triangle

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bf{Given:-}\begin{cases}\sf{Perimeter\:of\: similar\: triangle}\\ \sf{12cm\:and 72cm}\\ \sf{Area:-}\\ \sf{ 6cm{}^{2}and \:?}\end{cases}$

We have to find the Area of bigger triangle

Now we know that :-

$\boxed{\sf{\frac{Area\:of\:smaller\triangle}{Area\:of\:larger\triangle}=\frac{(Perimeter\:of\: smaller\triangle){}^{2}}{(Perimeter\:of\: larger\triangle){}^{2}}}}}$

So

$\bf\underline{\red{According\:To\: Question:-}}$

$\sf:\implies Put\:the\:value\:which \:is\: given\\ \\ \sf:\implies \dfrac{6cm{}^{2}}{x}=\dfrac{12\times 12}{72\times 72}\\ \\ \sf:\implies Now \:cross\: multiplication\\ \\ \sf:\implies 6\times 72\times =12\times 12\times x\\ \\ \sf:\implies \dfrac{6\times\cancel{72}\times \cancel{72}}{\cancel{12}\times \cancel{12}}=x\\ \\ \sf:\implies 6\times 6\times 6=x\\ \\ \sf:\implies x=216cm{}^{2}$

$\boxed{\sf{\blue{Area\:of\: bigger\triangle=216cm{}^{2}}}}$