Concept
The perimeter of a rectangle is the sum of all the length of its outer boundary.
Here, we use the perimeter formula to calculate the answer.
Perimeter of a rectangle formula = 2 (Length) + 2 (Breadth)
Next, List all the data from the question.
Length = 5z
Breadth = 4z + 3
Perimeter = 222
Substitute Length, Breadth and perimeter to find the value of z.
222 = 2(5z) + 2(4z + 3)
222 = 10z + 8z + 6
collect like terms
222 - 6 = 18z
216 = 18z
Divide both sides by 18
[tex]\begin{gathered} \frac{216}{18}\text{ = }\frac{18z}{18} \\ z\text{ = 12} \end{gathered}[/tex]Next, find the length and breadth
Length = 5z
= 5 x 12
= 60
Breadth = 4z + 3
= 4(12) + 3
= 48 + 3
= 51
AD = BC = 51
Final answer AD = 51
