Question

A plot of land shaped as a right triangle has a base of 80 feet and an area of 6000 square feet. What is the length, in feet, of the hypotenuse of the triangular plot?

Answer 1

h = 170 ft

Explanation:

Let A represent the area, b the base and h the height of this triangle. The area formula is

A = (1/2)(b)(h).

Here A = 6000 ft^2 = (1/2)(80 ft)(h).

Solve this for the height, (h):

6000 ft^2 = (40 ft)(h), or

6000 ft^2

h = ---------------- = 150 ft

40 ft

Now we know the leg lengths: 150 ft and 80 ft.

Use the Pythagorean Theorem to find the length of the hypotenuse:

h^2 = 80^2 + 150^2, or

h^2 = 6400 +22500 = 28900

Taking the square root of this figure, we get the length of the hypotenuse:

h = 170 ft