Question

The perimeter of the rectangle below is 112 units. Find the length of side VW . Write your answer without variables. Top YX: 4z Left YV: 5z + 2 Right XW: (blank) Bottom VW: (blank)

Answer 1

`VW = 33`

Explanation:

See attachment for complete question

Given

`VY = 4x - 1`

`VW = 5x + 3`

`Perimeter = 112`

Required

Determine the length of VW

Perimeter is calculated as:

`Perimeter = 2 * (Width + Length)`

This gives:

`Perimeter = 2 * (VW + VY)`

Substitute values for VW, VY and Perimeter

`112 = 2 * (4x - 1 + 5x + 3)`

Collect Like Terms

`112 = 2 * (4x + 5x -1 +3)`

`112 = 2 * (9x +2)`

Divide through by 2

`56 = 9x + 2`

Collect Like Terms

`9x = 56 - 2`

`9x = 54`

`x = 54/9`

`x = 6`

Substitute 6 for x in
`VW = 5x + 3`

`VW = 5 * 6 + 3`

`VW = 30 + 3`

`VW = 33`