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 two small sides are 8 cm and 15 cm, then the area of the blue square is _____.

• A. 289 $c{m}^2$
• B. 578 $c{m}^2$
• C. 143 $c{m}^2$
• D. 144.5 $c{m}^2$

Answer 1

The correct option is A

289 $c{m}^2$

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

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

$\Rightarrow (Hypotenuse{)}^2=8^2+{15}^2$

$\Rightarrow (Hypotenuse{)}^2=64+225=289$

$\Rightarrow \left(Hypotenuse\right)=17$

The area of the blue square = ${17}^2=289c{m}^2$