Explanation:
The perimeter of a rectangle is the sum of all the sides and the width sides are equal, as well as the two length sides.
For this problem that would mean that two sides are equal to BC and two sides are equal to AB.
Since the perimeter (P) is equal to 60 , we can write:
P = 2 * BC + 2 * AB
We can substitute the expressions we are given for AB and BC and 60 for the perimeter:
60 = 2 (2z + 3 ) + 2 (3z + 2)
Using the distributive property and combining like terms, we can find the value of the variable , z:
60 = 4z + 6 + 6z + 4
60 = 10z + 10
Subtract 10 from both sides of the equation:
60 - 10 = 10z + 10 -110
50 = 10z
Divide both sides of the equation by 10:
50/10 = 10z/10
5 = z
Since z = 5, then BC is 2z + 3 or 2*5 + 3
BC = 13
Tell me if that's correct!