Question

Refer to the following figure. Three squares are constructed on each side of a right angled triangle as shown, with the side of each square equal to the length of the side on which it is constructed. If the largest side measures 13 units, then the sum of the areas of the three squares is :

• A. 169 sq. units
• B. 338 sq. units
• C. 625 sq. units
• D. 576 sq. units

Answer 1

The correct option is B 338 sq. units

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

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

${13}^2$ = $a^2$ + $b^2$ = 169...(1)

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 (1))

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