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 colour 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,

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

${13}^2$ = $a^2$ + $b^2$ = 169 ------------------- (I)

Now,

Sum of the areas of the three squares =${\left(sideofyellowsquare\right)}^2$ + ${\left(sideofbrownishsquare\right)}^2$ +

${\left(sideofbluesquare\right)}^2$

Sum of the areas of the three squares =$a^2$ + $b^2$ + ${13}^2$ = ${13}^2$ + ${13}^2$ (from (I))

Sum of the areas of the three squares = 169 + 169 = 338.