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?

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

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 :

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,

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

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

Thus, (C) is the correct option.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

if i put something wrong your not gonna like it so rather not say nothing.