Question

The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length? Width = a0 inches Length = a1 inches

Answer 1

width = 15 inches

Length = 20 inches

That's your answer!!

Answer 2

Width = 15 inches Length = 20 inches

Explanation:

The area of a rectangle is calculated using the following formula.

`A = Lx` (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:

`L = x + 5` (2)

Also The area of a rectangle can be represented by the equation
`x^2 + 5x = 300`

so to find the width x we solve the equation

`x^2 + 5x -300=0` (3)

For an equation of the form
`ax ^ 2 + bx + c = 0` the quadratic formula is:

`x=(-b\±√(b^2-4ac))/(2a)`

In this case note that:

`a=1\\b=5\\c=-300`

Then:

`x=(-5\±√((5)^2-4(1)(-300)))/(2(1))`

`x=(-5\±√(25+1200))/(2)`

`x=(-5\±√(1225))/(2)`

`x=(-5\±35)/(2)`

`x_1=(-5+35)/(2)` →
`x_1=15`

`x_2=(-5-35)/(2)` →
`x_2=-20`

We take the positive solution
`x=15\ in`

Now we use equation (2) to find L

`L = x + 5`

`L = 15 + 5`

`L = 20\ in`