Question

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is $13,$ sum of the areas of the three squares is ___. [The angle opposite to the blue coloured square is the right angle]

Answer 1

Let the other two sides of the triangle be $a$ and $b.$ Since, the largest side is the hypotenuse, we have, by Pythagoras theorem,

${\text{Hypotenuse}}^2=a^2+b^2$

$\Rightarrow {13}^2=a^2+b^2=169$ ... (i)

Now,

Sum of the areas of the three squares $={\text{(side of yellow square)}}^2+{\text{(side of brownish square)}}^2+{\text{(side of blue square)}}^2$

$=a^2+b^2+{13}^2={13}^2+{13}^2$ [from (i)]

So, sum of the areas of the three squares $=169+169=338$