Question

The length of a rectangular frame is represented by the expression 2x+4 , and the width of the rectangular frame is represented by the expression 2x+10. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches.

Answer 1

Given:

Given that the length of a rectangular frame is (2x + 4)

The width of the rectangular frame is (2x + 10)

The area of the rectangular frame is 120 square inches.

We need to determine an equation to solve the width of the rectangular frame.

Equation for width of the rectangular frame:

The value of x can be determined using the area of the rectangle formula.

Thus, we have;

`A=length * width`

Substituting the values, we have;

`120=(2x +4)(2x+10)`

`120=4x^2+20x+8x+40`

`120=4x^2+28x+40`

Subtracting both sides by 120, we have;

`0=4x^2+28x-80`

Thus, the equation for the width of the rectangular frame is
`4x^2+28x-80=0`