Question

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: 4x^2+32x-80=0
B: 4x^2+32x+60=0
C: 2x^2+32x-80=0
D: x^2+16x+60=0​

Answer 1

A: 4x² + 32x - 80 = 0

Explanation:

• Length = 2x + 10 in
• Width = 2x + 6 in
• Area = 140 in²

Formula

• Area (rectangle) = Length x Width

Solving :

• 140 = (2x + 10)(2x + 6)

• 2x(2x) + 10(2x) + 2x(6) + 10(6) = 140

• 4x² + 20x + 12x + 60 = 140
• 4x² + 32x - 80 = 0
• The correct option is A

Answer 2

A

Explanation:

the area (A) of a rectangle is calculated as

A = length × width

= (2x + 10)(2x + 6) ← expand using FOIL and equate to 140

= 4x² + 12x + 20x + 60 = 140

= 4x² + 32x + 60 = 140 ( subtract 140 from both sides )

4x² + 32x - 80 = 0