Question

There are 3 squares which are arranged in such a manner that it forms a triangle as shown in the figure below. If the area of square A and B is $81c{m}^2$ and $144c{m}^2$ respectively, then find the area of the third square C.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We know that the area of a square is equal to ${\left(side\right)}^2$ . So, if the area of square A is 81 $c{m}^2$ , then side (XY) is 9 cm and if the area of square B is 144$c{m}^2$ , then side (YZ) is 12 cm. Thus, in triangle XYZ, side (XY) = 9cm and side (YZ) = 12 cm.

Using Pythagoras theorem, we get:

${\left(XY\right)}^2+{\left(YZ\right)}^2={\left(XZ\right)}^2{\left(9cm\right)}^2+{\left(12cm\right)}^2={\left(XZ\right)}^{2}81c{m}^2+144c{m}^2=225c{m}^{2}Thus,areaofsquareCis225c{m}^2$.