Answer:
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
