Answer:
The answer is b = 30 ft and h = 40 ft.
Step-by-step explanation:
Given:
The height of a parallelogram is 10ft more than its base
The area is 1200 ft².
Now, to solve for b and h.
Let the base (b) be [tex]x.[/tex]
And the height (h) is = [tex]x+10.[/tex]
Area = 1200 ft².
Now, to solve we put formula of area:
[tex]Area =b\times h[/tex]
[tex]1200=x\times (x+10)[/tex]
[tex]1200=x^2+10x[/tex]
Subtracting both sides by 1200 we get:
[tex]0=x^2+10x-1200\\x^2+10x-1200=0[/tex]
Now, solving the quadratic equation:
[tex]x^2+40x-30x-1200=0[/tex]
[tex]x(x+40)-30(x+40)=0[/tex]
[tex](x+40)(x-30)=0[/tex]
[tex]x+40=0[/tex] and [tex]x-30=0[/tex]
Subtracting Adding both sides
both sides by 30 we get:
by 40 we get:
[tex]x=-40.[/tex] [tex]x=30.[/tex]
So, we will take the positive result.
[tex]x=30.[/tex]
Thus, the base (b) = 30 ft.
Now, getting the height (h) by substituting the value of [tex]x[/tex]:
[tex]x+10\\=30+10\\=40\ ft.[/tex]
Therefore, the answer is b = 30 ft and h = 40 ft.
