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. Find the sum of the areas of the three squares if the largest side is 13 and the angle opposite to the blue colour square is right angle.

• A. 169
• B. 338
• C. 159
• D. 318

Answer 1

The correct option is B 338

Since the largest side is the hypotenuse, let the other two sides of the triangle be a and b.

Now, a, b and hypotenuse becomes the sides of yellow square, brownish square and blue square.

By Pythagoras theorem,

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

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

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.