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;
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]120=(2x +4)(2x+10)[/tex]
[tex]120=4x^2+20x+8x+40[/tex]
[tex]120=4x^2+28x+40[/tex]
Subtracting both sides by 120, we have;
[tex]0=4x^2+28x-80[/tex]
Thus, the equation for the width of the rectangular frame is [tex]4x^2+28x-80=0[/tex]
