Question

The perimeter of the rectangle below is 222 units. Find the length of side AD.Write your answer without variables.DС4z + 3AD =- UА5zB

Answer 1

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

`\begin{gathered} (216)/(18)\text{ = }(18z)/(18) \\ z\text{ = 12} \end{gathered}`

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