229k views
5 votes
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.

User LuizMello
by
5.2k points

1 Answer

6 votes

Answer:

  • 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.

User Sufian Latif
by
5.6k points