Answer:
Length of the base = 10
Length of the height = 4
Step-by-step explanation:
Remember that the area of a triangle is given by the formula
[tex]A=\frac{1}{2} bh[/tex]
where
[tex]A[/tex] is the area
[tex]b[/tex] is the base
[tex]h[/tex] is the height
We know from our problem that the base of the triangle is 2x + 2, so [tex]b=2x+2[/tex]. We also know that its height is x and its area is 20 ft^2, so [tex]h=x[/tex] and [tex]A=20[/tex]. Let's replace the values in our formula to find [tex]x[/tex]:
[tex]A=\frac{1}{2} bh[/tex]
[tex]20=(\frac{1}{2} )(2x+2)(x)[/tex]
[tex]20=(\frac{1}{2} )2(x+1)(x)[/tex]
[tex]20=x(x+1)[/tex]
[tex]20=x^2+x[/tex]
[tex]x^2+x-20=0[/tex]
[tex](x-4)(x+5)=0[/tex]
[tex]x=4[/tex] or [tex]x=-5[/tex]
Since distance cannot be negative, [tex]x=4[/tex]
Now we can substitute the value for [tex]x[/tex] in the base and height:
base = [tex]2x+2[/tex]
base = [tex]2(4)+2[/tex]
base = [tex]8+2[/tex]
base = [tex]10[/tex]
height = [tex]x[/tex]
height = [tex]4[/tex]
