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

Answer:

$VW = 33$

Step-by-step 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 $VW = 5x + 3$

$VW = 5 * 6 + 3$

$VW = 30 + 3$

$VW = 33$