Question

A park in the shape of a right triangle is set in the middle of 3 square rose gardens, with one garden along each side. Which statement is true about the 3 gardens?

A) The area of Garden B minus the area of Garden C is equal to the area of Garden A.
B) The area of Garden B plus the area of Garden C is equal to twice the area of Garden A.
C) The area of Garden C minus the area of Garden B equals the area of Garden A.
D) The area of Garden C minus the area of Garden A is equal to twice the area of Garden B.

Answer 1

The answer would be C. This is because of Pythagorean theorem. A^2 + B^2=C^2

Answer 2

The area of Garden C minus the area of Garden B equals the area of Garden A.

Thus, (C) is the correct option.

Explanation:

In the figure below, PQR is a right angle triangle with right angle at R and A is perpendicular , B is base and C is hypotenuse of the triangle.

One square garden along each side of triangle.

Area of square = Side × Side

So area of each square garden is :

A × A = A²

B × B = B²

C × C = C²

According to Pythagoras theorem,

In a right angle triangle, square of hypotenuse is equal to sum of square of the remaining two sides.

By figure,

A² + B² = C²

Area of garden A + area of garden B = Area of garden C

A² = C² -B²

The area of Garden C minus the area of Garden B equals the area of Garden A.

Thus, (C) is the correct option.