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 coloured square is the right angle. If the largest side is 5 cm, then find the sum of the areas of the yellow square and brown square.

Answer 1

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

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

$\Rightarrow 5^2=a^2+b^2$

$\Rightarrow 25=a^2+b^2.....\left(i\right)$

$\text{Sum of the areas of the yellow square and brown square}=\text{Area of the blue square}$

$\therefore$ The sum of areas of the yellow and brown square = $25c{m}^2$