The perimeter of the rectangle below is 54 units find the length of side BC. Write without variables
side AB is 3Z +3 side BC is 2Z-1
3 z + 3 + 2 z - 1 = 54/2
To find the length of side BC without using variables, we can substitute the expressions for side AB and side BC into the equation for the perimeter of a rectangle.
Given:
Perimeter = 54 units
Side AB = 3Z + 3
Side BC = 2Z - 1
Perimeter = 2(Side AB + Side BC)
Substituting the given expressions:
54 = 2((3Z + 3) + (2Z - 1))
Simplifying the expression inside the parentheses:
54 = 2(5Z + 2)
Distributing 2 to each term inside the parentheses:
54 = 10Z + 4
Subtracting 4 from both sides:
50 = 10Z
Dividing both sides by 10:
5 = Z
With Z = 5, we can find the length of side BC by substituting Z into the expression for side BC:
Side BC = 2Z - 1
= 2(5) - 1
= 10 - 1
= 9
Therefore, the length of side BC is 9 units.
To find the length of side BC without using variables, we need to express the length in terms of a constant value.
Given the information that the perimeter of the rectangle is 54 units, we can use the formula for the perimeter of a rectangle, which is the sum of all four sides.
The formulas for the lengths of the sides are given as:
Side AB = 3Z + 3
Side BC = 2Z - 1
To find the length of side BC without variables, let's substitute the given formulas into the perimeter formula:
Perimeter = Side AB + Side BC + Side AB + Side BC
54 = (3Z + 3) + (2Z - 1) + (3Z + 3) + (2Z - 1)
Now, we can start simplifying the equation by combining like terms:
54 = 3Z + 3 + 2Z - 1 + 3Z + 3 + 2Z - 1
Combining like terms:
54 = 10Z + 4
To isolate the variable Z, we can subtract 4 from both sides of the equation:
54 - 4 = 10Z + 4 - 4
50 = 10Z
Finally, we can solve for Z by dividing both sides of the equation by 10:
50 / 10 = 10Z / 10
5 = Z
Now, we substitute the value of Z back into the formula for side BC:
Side BC = 2Z - 1
Side BC = 2(5) - 1
Side BC = 10 - 1
Side BC = 9
Therefore, the length of side BC is 9 units.