Question

A triangle has a base length of (2x - 4) units and a height of (x + 5) units. Write and solve a quadratic equation to determine what value of x gives the triangle an area of 44 square units

Answer 1

x=6

Explanation:

`(1)/(2) (2x-4)(x+5)=44\\(x-2)(x+5)=44`

`x^(2) -2x+5x-10=44\\x^(2) +3x-54=0`

`x^(2) +9x-6x-54=0\\x(x+9)-6(x+9)=0\\(x+9)(x-6)=0\\x=-9(rejected),6`

side is 2×6-4=8 units

height=x+5=6+5=11 units

x=-9 is rejected because it gives negative side and negative height.

Answer 2

x = -9

x = 6 BUT IT DOES NOT WORK WHEN YOU PLUG IT BACK IN

Explanation:

Triangle area = 1/2 bh

The area is given (44)

base = 2x-4

height = x+5

44 = 1/2 (2x-4) (x+5)

Distribute

44 = 1/2 (2x^2 + 10x - 4x - 20)

44 = 1/2 (2x^2 + 6x - 20)

Take out a 2

44 = 2 * 1/2 (x^2 + 3x - 10)

44 = x^2 + 3x - 10

Subtract 44

0 = x^2 + 3x - 54

Factor the way you like and you should get

(x + 9) (x - 6)

x = -9

x = 6

If you plug them in only the -9 works.

44 = 1/2 (-22) (-4)