A triangle With an area of 85 square inches has a height that is three less than two times the base find the base and the height

Answer 1

The formula for area of a triangle🔺 is A=1/2*b* h

Given info:

A=85 in²

h=2*b-3 (the height is 3 less than two times the base)

1. Rewrite formula in terms of one variable A=1/2b*(2b-3)
2. Plug in given information 85=1/2b*(2b-3)
3. solve for b in the quadratic equation above 2b²-3b-170=0
4. (2b+17)(b-10)=0
5. b=10, b≠-17/2
6. Plug back in to h=2b-3. h=2(10)-3=17
7. b= 10in; h=17in

Answer 2

let x be the length of the base

then the height = 2x-3 (three less than two times the base)

area of triangle = 1/2 * base * height

1/2 * x * (2x-3) = 85

x * (2x-3) = 170

2x**2 - 3x = 170

2x**2 - 3x -170 = 0

using quadratic formula with a=2, b=-3 and c=-170

x = 10 or -8.5

x = 10 is only logical choice and that is the base

2x-3 = 17 is the height

check 1/2 *10 * 17 = 85