Answer:
PQ = 24
Explanation:
The perimeter of the rectangle is 86, and we know that its opposite sides are the same lengths. So, we get this equation.
( 2z + 3 ) + ( 2z + 3 ) + ( 3z ) + ( 3z ) = 86
Remove the parentheses.
2z + 3 + 2z + 3 + 3z + 3z = 86
Collect like terms and calculate.
10z + 6 = 86
Move the constant to the right.
10z = 86 - 6
10z = 80
Divide both sides by 10.
z = 8
Now, we want PQ which is "3z".
PQ = 3 × z
= 3 × 8
= 24
That is the answer.
I hope it helps.