the perimeter of the rectangle below is 78 units. Find the length of side VY. Write your answer without variables

the length of side BC is 18 units

Step-by-step explanation:

Perimeter of the rectangle: P=76 units

AB=4z

BC=3z+3=?

We need to determine z

The formula to calculate the perimeter of a rectangle is:

P=2(w+l)

Width: w=AB=4z

Length: l=BC=3z+3

Replacing in the formula:

76 = 2 [4z+(3z+3)]

Eliminating the parentheses:

76 = 2 [4z+3z+3]

Adding like terms:

76 = 2 (7z+3)

Solving for z: Dividing both sides of the equation by 2:

76 / 2 = 2 (7z+3) / 2

38 = 7z+3

Subtracting 3 both sides of the equation:

38-3 = 7z+3-3

Subtracting:

35 = 7z

Dividing both sides of the equation by 7:

35 / 7 = 7z / 7

Dividing:

5 = z

z = 5

Then:

BC=3z+3

Replacing z by 5 in the formula above:

BC = 3(5)+3

Multiplying:

BC = 15 + 3

Adding:

BC = 18 units

x

step-by-step explanation: