Question

The floor of a shed given on the right has an area of 52 square feet. The floor is in the shape of a rectangle whose length is 5 feet less than twice the width. Find the length and the width of the floor of the shed.

Answer 1

13/2 feet width and 8 feet length

Explanation:

We have that the area of a rectangle is as follows:

ar = l * w

we know that the value of the area is 52 ft ^ 2, therefore:

l * w = 52

According to the statement we have to:

x = width

2 * x - 5 = length

we replace in the area formula and we have to:

x * (2 * x - 5) = 52

We solve and we are left with:

2 * x ^ 2 - 5 * x - 52 = 0

Factoring the above we are left with:

(2 * x - 13) * (x + 4) = 0

(x + 4) = 0, it means that x = -4, a negative number, therefore this option cannot be.

2 * x - 13 = 0

x = 2/13, would be the width

the length:

2 * x - 5 = 2 * (2/13) - 5 = 8

What the measurements mean is 13/2 feet width and 8 feet length