SOLUTION: The base of a triangle is 5 inches shorter than twice its height. If the area of this triangle is 114 square inches, find the length of the base and the height of this triangle.

Algebra ->  Triangles -> SOLUTION: The base of a triangle is 5 inches shorter than twice its height. If the area of this triangle is 114 square inches, find the length of the base and the height of this triangle.      Log On


   

Question 996129: The base of a triangle is 5 inches shorter than twice its height. If the area of this triangle is 114 square inches, find the length of the base and the height of this triangle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
b, base
h, height
b=h-5

Formula for area triangle, %281%2F2%29bh
%281%2F2%29bh=114
%281%2F2%29%28h-5%29h=114
h%5E2-5h=228
h%5E2-5h-228%29=0

Discriminant, 25%2B4%2A228=937, a prime number.

highlight%28h=%285%2Bsqrt%28937%29%29%2F2%29, taking the PLUS form from the formula for solution of quadratic equation. Use this to evaluate b.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

The base of a triangle is 5 inches shorter than twice its height. If the area of this triangle is 114 square inches, find the length of the base and the height of this triangle.
Height: highlight_green%2812%29 inches

Length of base: 2(12) - 5, or 24 - 5, or highlight_green%2819%29 inches