Question

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 small two sides are 5 cm and 12 cm, then find the area of the blue square.

• A. 289 $c{m}^2$
• B. 169 $c{m}^2$
• C. 64 $c{m}^2$
• D. 225 $c{m}^2$

Answer 1

The correct option is B

169 $c{m}^2$

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

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

$\Rightarrow (Hypotenuse{)}^2=5^2+{12}^2$

$\Rightarrow (Hypotenuse{)}^2=25+144=169$

$\Rightarrow \left(Hypotenuse\right)=13$

The area of the blue square = ${13}^2=169c{m}^2$