Question

3. The width and length of a rectangle are

consecutive integers. If the perimeter of
the rectangle is 142 inches, find the width
and length of the rectangle.​

Answer 1

The dimensions of the rectangle are 35 inches by 36 inches.

Explanation:

If the length and width are consecutive integers and L=n, then W=n+1 assuming the width is larger.

We are given the perimeter is 142 inches so: 2L+2W=142.

Substituting L=n and W=n+1 we have: 2(n)+2(n+1)=142.

Let's solve it:

2(n)+2(n+1)=142

Distribute:

2n+2n+2=142

Combine like terms:

4n+2=142

Subtract 2 on both sides:

4n=140

Divide both sides by 4:

n=140/4

n=35

Since L=n, then the length is 35 inches.

Since W=n+1, then the width is 36 inches.

The dimensions of the rectangle are 35 inches by 36 inches.

Answer 2

35 and 36

Explanation:

If the smaller dimension is x, then the larger dimension is x + 1. Therefore:

2x + 2(x + 1) = 142

2x + 2x + 2 = 142

4x = 140

x = 35

One dimension is 35, and the other dimension is 36.