Question

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Answer 1

The value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.

How to determine the dimensions?

The given parameters are:

Base = 5(x+3)

Height = 2(x+9)

Perimeter = 108

The perimeter of a rectangle is

P = 2 *(Base + Height)

So, we have:

2 *(5(x + 3) + 2(x + 9)) = 108

Divide both sides by 2

5(x + 3) + 2(x + 9) = 54

Open the brackets

5x + 15 + 2x + 18 = 54

Evaluate the like terms

7x = 21

Divide by 7

x = 3

Substitute x = 3 in Base = 5(x+3) and Height = 2(x+9)

Base = 5(3+3) = 30

Height = 2(3+9) = 24

Hence, the value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.

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