Question

The length of a rectangle is x feet more than its width. The area of the rectangle is 5x + 25. What is the width of the rectangle?

Answer 1

w =
`l + (25 - l^(2))/(l - 5)`

(Anyone can correct me if I'm wrong)

Explanation:

Before we start the solving, we can make the following statements:

Area = l x w

Area = 5x + 25

therefore,

l x w = 5x + 25

Since the question states that the length is x more than the width, so we can make the following statement:

w = l + x

With this, we can substitute it to the first statement we made, l x w = 5x + 25,

l x (l + x) = 5x + 25

`l^(2)` + lx = 5x + 25

lx - 5x = 25 -
`l^(2)`

x(l - 5) = 25 -
`l^(2)`

x =
`(25 - l^(2))/(l - 5)`

From this, we can find w by substituting it in the statement we made earlier, w = l + x,

w =
`l + (25 - l^(2))/(l - 5)`