The length of the rectange is 20ft and width of the 5ft.
Step-by-step explanation:
Let us consider a rectangle and its area is known to be 100 sq ft.
We are given the information that the length of the rectangle is 10ft longer than twice its width.
⇒Length l = 2w+10.
Where w is the width of the rectangle.
The formula for area of the rectangle A = length × width.
A= (2w+10)×w.
100 = [tex]2w^2+10w[/tex].
0=[tex]2w^2+10w-100[/tex].
Thus it forms an quadratic equation we have to solve for the solution.
0=(2w-10)(w+10).
2w-10=0. w+10=0.
2w=10. w=-10. (negative value cannot be choosed.)
w=[tex](\frac{10}{2} )[/tex].
w=5ft.
Thus width is is 5 ft.
Length = 2(5)+10.
=10+10.
=20ft.
Thus the length is 20ft.
