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 cm, sum of the areas of the three squares is___. The angle opposite to the blue colour square is the right angle.

Answer 1

Let the other two sides of the triangle be a and b.
By Pythagoras theorem,
(Hypotenuse)${}^2$ = a${}^2$ + b${}^2$
$\Rightarrow {13}^2=a^2+b^2=169--------\left(I\right)$
Sum of the areas of the three squares = (side of yellow square)${}^2$ + (side of brown square)${}^2$ + (side of blue square)${}^2$
Sum of the areas of the three squares
= $a^2+b^2+{13}^2={13}^2+{13}^2\text{(from (I))}$
Therefore, sum of the areas of the three squares = 169 + 169 = 338 ${\text{cm}}^2$