Question

Examine the rectangle at right.

A. Write an expression for the perimeter in terms of x.
B. Assuming the perimeter is 78 cm, determine the dimensions of the rectangle. Show all of your work.
C. Verify that the area of this rectangle is 360 . Explain how you know this.​

Answer 1

• A. The expression for the perimeter is 6x.
• B. The dimensions of the rectangle are 13 cm and 26 cm.
• C. The area of the rectangle is 338 cm².

Step-by-step explanation:

A. The perimeter of a rectangle is the sum of all its side lengths. In this case, the rectangle has two sides of length x and two sides of length 2x. So the expression for the perimeter, P, is:

P = x + x + 2x + 2x = 6x

B. We are given that the perimeter is 78 cm. Setting up the equation:

6x = 78

Solving for x:

x = 13 cm

The dimensions of the rectangle are x = 13 cm and 2x = 26 cm.

C. The area of a rectangle is found by multiplying its length and width. In this case, the length is x and the width is 2x. So the expression for the area, A, is:

A = x * 2x = 2x²

Plugging in the value of x:

A = 2 * 13² = 338 cm²

The area of the rectangle is not 360 cm² as stated in the question.