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 st
atement 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.
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.
2 answers:
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:
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.
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