the perimeter of the rectangle below is 74 units find the length of side pq
sr is the top 2z-1 side is sp 3z+3 pq is the bottom
74 = 2(2z-1) + 2(3z+ 3)
37 = 2z -1 + 3 z + 3
35 = 5 z
z = 7
the bottom of the rectangle is the same as the top 2 z - 1
= 14 - 1
= 13
To find the length of side PQ of the rectangle, we need to set up an equation using the given information about the perimeter.
First, let's identify the sides of the rectangle:
- SR represents the top side, which has a length of 2z-1.
- SP represents the right side, which has a length of 3z+3.
- PQ represents the bottom side, which we want to find the length of.
Now, let's set up the equation for the perimeter:
Perimeter = sum of all sides
We know that the perimeter is 74 units, so we can write:
74 = SR + SP + PQ
Substituting the given expressions for SR and SP:
74 = (2z-1) + (3z+3) + PQ
Simplifying the equation:
74 = 2z + 3z + 2 - 1 + PQ
74 = 5z + 1 + PQ
To find PQ, we need to isolate it on one side of the equation. Let's move the terms that don't involve PQ to the other side:
PQ = 74 - 5z - 1
PQ = 73 - 5z
Therefore, the length of side PQ is given by the expression 73 - 5z.