Question

. The perimeter of a rectangle is 44 centimeters. The length of the rectangle can be

represented by (7x – 4) and its width can be represented by (x + 2). Which of the following
best represents the value of x?

Answer 1

The value of x is 3, which is found by setting up an equation based on the perimeter formula for a rectangle, simplifying, and solving for x.

Step-by-step explanation:

The perimeter of a rectangle is 44 centimeters. The length of the rectangle can be represented by (7x – 4) and its width can be represented by (x + 2). To find the value of x, we can set up an equation using the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width:

• Write the equation for the perimeter: 44 = 2(7x – 4) + 2(x + 2).
• Simplify and solve for x: 44 = 14x – 8 + 2x + 4.
• Simplify further: 44 = 16x – 4.
• Add 4 to both sides: 48 = 16x.
• Divide both sides by 16: x = 3.

So, the value of x is 3.