Question

The perimeter of a rectangle is 8(2x+1) inches. The length of the sides of the rectangle are 3x+4 inches and 4x+3 inches. Find the length of each side of the rectangle. (You will have two answers.)

Answer 1

The lengths of the sides of the rectangle are 13 inches and 15 inches

Explanation:

The perimeter of a rectangle

Given the two sides of a rectangle a and b. The perimeter of the rectangle is:

`P=2(a+b)`

We are given the perimeter of a rectangle as:

`P=8(2x+1)`

And each side has a length of 3x+4 and 4x+3. Calculating the perimeter:

`P=2(3x+4+4x+3)=2(7x+7)`

We set up the equation:

`8(2x+1)=2(7x+7)`

Dividing by 2:

`4(2x+1)=7x+7`

Operating:

`8x+4=7x+7`

Subtracting 7x:

`x+4=7`

Subtracting 4:

x=3

The length of each side is:

3x+4=3*3+4=13

4x+3=4*3+3=15

The lengths of the sides of the rectangle are 13 inches and 15 inches