Question

1 A rectangle has a length of (x + 3) centimeters and a width of \frac{1}{2} 2 1 ​ x centimeters. If the perimeter is 24 centimeters, what is the length of the rectangle?

Answer 1

9cm

Explanation:

Perimeter of a rectangle = 2(L+W)

L is the length = x+3 cm

W is the width = 1/2 x cm

Perimeter = 24cm

Substitute into the equation;

P = 2(x+3+ 1/2 x)

P = 2(3/2x + 3)

24 = 2(3x/2 + 3)

Expand

24 = 3x + 6

3x = 24 - 6

3x = 18

x = 18/3

x = 6

Since L = x+3

L = 6+3

L = 9cm

Hence the length of the rectangle is 9cm