Question

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

Answer 1

Complete 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.

Correct Answer:

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

Thus, (C) is the correct option.      

Step-by-step explanation:

According to question , 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 :

$A ( A) = A^2\\B ( B) = B^2\\C ( C )= C^2$

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,

$A^2 + B^2 = C^2$

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

$A^2 = C^2 -B^2$

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

Thus, (C) is the correct option.