Indian Institute of Foreign Trade 2012 Solved Paper

Hypotenuse = 97 m and perimeter = 234 m
Let the other two sides be a m and b m
So $\mathit{a}+\mathit{b}=\left(234-97\right)\mathit{m}=137\mathit{m}$....(i)
Also, by Pythagoras Theorem,${\mathit{a}}^2+{\mathit{b}}^2={97}^2$
Or ${\left(\mathit{a}+\mathit{b}\right)}^2-2\mathit{a}\mathit{b}=9409$
Or,$2\mathit{a}\mathit{b}={137}^2-9409$
Or,$2\mathit{a}\mathit{b}=9360$...(ii)
${\left(\mathit{a}-\mathit{b}\right)}^2={\mathit{a}}^2+{\mathit{b}}^2-2\mathit{a}\mathit{b}={97}^2+9360=49$
So,$\left(\mathit{a}-\mathit{b}\right)=7$ [Assuming a > b]....(iii)
Solving (i) and (iii), we get
a =72 m and b = 65m
Hence, option B is the correct answer.