Question

A rectangle has a width of 2.5 inches and a length of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle.

Answer 1

To find the length of the rectangle, we can set up an equation using the perimeter and area formulas. The length is determined to be 10 inches.

Step-by-step explanation:

To solve this problem, we can use the given information to set up an equation. The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. The area of a rectangle is given by the formula A = lw. The problem states that the perimeter is equal to the area, so we can set up the equation 2l + 2w = lw.

Substituting the given values of w = 2.5 and l = x, we have 2(x) + 2(2.5) = 2.5x.

Simplifying, we get 2x + 5 = 2.5x.

Subtracting 2x from both sides, we get 5 = 0.5x.

Dividing both sides by 0.5, we get x = 10.

So the length of the rectangle is 10 inches.