Question

The length of a rectangular picture frame is twice the width. The frame has a perimeter of 96 inches. Write and solve a

system of equations to represent this solution. Let x represent the width of the frame, and let y represent the length of
the frame. Interpret the solution
(32, 16). The width of the frame is 32 inches, and the length of the frame is 16 inches.
(32, 16); The width of the frame is 16 inches, and the length of the frame is 32 inches.
(16, 32). The width of the frame is 32 inches, and the length of the frame is 16 inches.
(16, 32); The width of the frame is 16 inches, and the length of the frame is 32 inches.

Answer 1

Length = 16 inches

Width = 32 inches

Explanation:

Width of the frame is represented by x and length by y inches. It is given that length of the frame is twice the width. This means y is twice of x. So, we can write the equation as:

y = 2x Equation 1

Perimeter of a rectangle is defined as:

Perimeter = 2 ( Length + Width )

Since, perimeter of the picture frame is equal to 96, we can write the equation as:

2(x + y) = 96 Equation 2

Substituting the value of y from Equation 1 in Equation 2, we get:

2(x + 2x) = 96

2(3x) = 96

6x = 96

x = 16

Substituting the value of x in Equation 1, we get:

y = 2x = 2(16) = 32

This means, the length of the rectangular picture frame is 16 inches and its width is 32 inches.

Answer 2

b

Explanation: