Question

The height of a triangle is 2 feet greater than the base. The area of the triangle is 199.5 square feet. Find the length of the base and the height of the triangle.

Answer 1

• base: 19 ft
• height: 21 ft

Explanation:

The area of a triangle is related to the base and height by ...

A = 1/2bh

Filling in the given information, we can find the base from ...

199.5 = (1/2)(b)(b+2)

399 = b^2 +2b . . . . multiply by 2

400 = (b +1)^2 . . . . add 1 to complete the square

20 = b +1 . . . . . . . . take the positive square root

19 = b . . . . . . . . . . . subtract 1

h = b+2 = 21

The base of the triangle is 19 feet and the height is 21 feet.