Question

The figure below is a rectangle with the dimensions given. If the perimeter of the rectangle is 48 cm, what are the

dimensions of the rectangle?
Х
3x

Answer 1

• L=3x
• B=x

Now

• 2(L+B)=48
• 2(x+3x)=48
• 2(4x)=48
• 8x=48
• x=6

B=6

L=3(6)=18

Answer 2

6 cm and 18 cm.

Explanation:

We are given that:

• Dimensions of rectangle: x and 3x
• Perimeter of rectangle: 48 cm

The perimeter of any rectangle is:

• L + W + L + W

To determine the dimensions of the rectangle, we need to determine the value of "x". The word "dimensions" are the length and the width of the rectangle. Since the question has not stated the length and width, we can consider the length as x and the width as 3x.

• ⇒ (x) + (3x) + (x) + (3x)

It is also given that the perimeter of the rectangle is 48 cm. Thus, the formula with the length and the width substituted is equivalent to 48 cm.

• ⇒ (x) + (3x) + (x) + (3x) = 48 cm

It is required for the expression on the left hand side to be simplified. This can be done by combining like terms.

• ⇒ x(1 + 3 + 1 + 3) = 48 cm
• ⇒ x(8) = 48 cm

Then, we can divide 8 both sides to isolate the coefficient from "x". Once the coefficient of "x" is isolated, we will obtain the value of "x".

• ⇒ x(8)/8 = 48/8
• ⇒ x = 6

Finally, substitute the value of "x" into the length and the width. We considered the length to be "x" and the width to be "3x". Therefore,

• ⇒ Length = x cm = 6 cm
• ⇒ Width = 3x cm = 3(6) cm = 18 cm

Thus, the dimensions of the rectangle are 6 cm and 18 cm.