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.
4x2 + 32x − 80 = 0
4x2 + 32x + 60 = 0
2x2 + 32x − 80 = 0
x2 + 16x + 60 = 0
The equation to solve for the width of the rectangular frame is:
(2x + 10)(2x + 6) = 140
Expanding and simplifying:
4x² + 32x + 60 = 140
4x² + 32x - 80 = 0
Therefore, the answer is:
4x² + 32x - 80 = 0
To find the equation that represents the width of the rectangular frame, we need to use the formula for the area of a rectangle: Area = length x width.
Given that the length is represented by the expression 2x + 10 and the total area is 140 square inches, we can set up the equation:
(2x + 10)(width) = 140
To solve for the width, we need to divide both sides of the equation by (2x + 10):
width = 140 / (2x + 10)
Therefore, none of the given equations (4x2 + 32x − 80 = 0, 4x2 + 32x + 60 = 0, 2x2 + 32x − 80 = 0, x2 + 16x + 60 = 0) is the correct equation to solve for the width of the rectangular frame with a total area of 140 square inches.