Question

I don't understand this one.

Adaline is designing a garden in the shape of q 45-45-90 degree triangle, with an area of 32 ft2. To the nearest foot, how much fencing will she need to enclose the garden?

A. 24 feet
B. 32 feet
C. 27 feet
D. 75 feet

Answer 1

C. 27 feet to the nearest foot.

Explanation:

In a 45-45-90 triangle the 2 legs ( the base and the height) are equal in length.

So the area = 1/2 * base * height

= 1/2 h^2 = 32

h^2 = 32 / 1/2 = 64

h = 8 feet.

That is both legs are 8 feet long.

So the amount of fencing needed = the perimeter

= 2*8 + H where H is the hypotenuse.

As it is a 45-45-90 triangle H = √ * 8 = 11.3 feet.

The perimeter = 16 + 11.3

= 27 feet to the nearest foot.