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 of the triangle on which it is constructed. The angle opposite to the blue colour square is the right angle. If the largest side is 17 cm, then find the sum of the areas of the three squares.

• A. 289 $c{m}^2$
• B. 578 $c{m}^2$
• C. 143 $c{m}^2$
• D. None

Answer 1

The correct option is B

578 $c{m}^2$

Let the other two sides of the triangle be a and b.
Since the largest side is the hypotenuse, By Pythagoras theorem,
$\left(\right(\text{Hypotenuse}{)}^2=a^2+b^2\Rightarrow {17}^2=a^2+b^2=289c{m}^2--------\left(I\right)$
$\text{Sum of the areas of the three squares}=(\text{side of yellow square}{)}^2+(\text{side of brown square}{)}^2+(\text{side of blue square}{)}^2$
Sum of the areas of the three squares = $a^2+b^2+{17}^2={17}^2+{17}^2$ (from (I)
$\therefore$ Sum of the areas of the three squares = $289+289=578c{m}^2$