the length of a rectangular frame is represented by the expression 2x + 10, and the width of the rectangular frame is represented by the expression 2x + 6. write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches.
a. 4x2 + 32x − 80 = 0
b. 4x2 + 32x + 60 = 0
c. 2x2 + 32x − 80 = 0
d. x2 + 16x + 60 = 0

is the required equation to calculate width of rectangular frame that has a total area of 140 square inches.

Given that,

Length of a rectangular frame is given as 2x + 10

Width of the rectangular frame is given as 2x + 6

Total area = 140 square inches

The area of rectangular frame is given as:

Plugging in values, we get

This is the required equation to calculate width of rectangular frame

Solve the above quadratic equation to get the value of "x"

Use the quadratic equation formula:

Here a = 4 ; b = 32 ; c = -80

x = 2 or x = -10

Now measurement cannot be negative, so taking the positve value of "x", we can calculate the width

So put "x" = 2

Width of the rectangular frame = 2x + 6 = 2(2) + 6 = 10

Thus the width of frame is 10 inches

step-by-step explanation: