Question

A rectangle patio that originally measured 5 feet by 10 feet was extended on one side each by x feet. The area of a new, larger, L-shaped extension is 126 feet.

Write an equation that could be used to solve for x.

Explain how you arrived at your equation.

Find the value of x by solving your equation.

Answer 1

We solve for the area of the original triangle and solution is shown below:
Original triangle area = LW = 5*10 = 20 squared units

If we extend this x on one side that resulted to L-shaped, we have the new area such as shown below:
New area = (L+X) (W)
126 = (5+x) * 10
126/10 = 5+x
12.6 - 5 = x
7.6 =x

I. The equation that could be used to solve for x is below:
126 = (5+x)*w
II. We arrived on this because of the statement that "x is added to one side that resulted to L-shaped rectangle, therefore it is added on 5 ft side"
III. The value of x is equal to 7.6 ft.