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.

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

Width is 16 inches and length is 32 inches.

Explanation:

Given: The length of a rectangular picture frame is twice the width. The frame has a perimeter of 96 inches.

To find: Length and width

Solution:

Let the x represent the width of the frame and y represent the length of the frame.

We have,

The perimeter of the frame is 96 inches.

length of the frame is twice its width, so
`y=2x`

Now,

`\text{Perimeter}=2(l+w)`

`\text{Perimeter}=2(y+x)`

`\text{Perimeter}=2(2x+x)`

`\text{Perimeter}=6x`

`\implies 6x=96`

`\implies x=16`

`y=2(16)=32`

So, width of the frame is 16 inches, and length of the rectangle is 32 inches