Respuesta :
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 :
[tex]A ( A) = A^2\\B ( B) = B^2\\C ( C )= C^2[/tex]
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,
[tex]A^2 + B^2 = C^2[/tex]
Area of garden A + area of garden B = Area of garden C
[tex]A^2 = C^2 -B^2[/tex]
The area of Garden C minus the area of Garden B equals the area of Garden A.
Thus, (C) is the correct option.
