Question

225 ft2

81 ft2

Three squares are joined below at their vertices to form a right triangle. Find X, the side
length of the square marked in the diagram.

12 feet

144 feet

48 feet

17.5 feet

Answer 1

12 ft

Explanation:

we know the areas of the 2 top squares.

the area of a square is simply the square of its side length.

=>

81 ft² means side length is 9 ft.

225 ft² means side length is 15 ft.

these are also 2 of the sides of the right triangle.

the third side we get by using Pythagoras :

c² = a² + b²

with c being the side opposite of the 90 degree angle.

so,

225 = 81 + x²

as x is also the third side of the triangle.

=> 144 = x²

x = 12 ft