Question

the length of a rectangle is three times its width. if the perimeter of the rectangle is 48 cm, find its length and width. length: cm width: cm

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ cm. Then the length $l$ is $3w$ cm (since length is three times the width).

Step2: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(l + w)$. We know $P = 48$ cm. Substitute $l = 3w$ into the formula:
$$48 = 2(3w + w)$$

Step3: Simplify and solve for $w$

First, simplify the expression inside the parentheses: $3w + w = 4w$. So the equation becomes:
$$48 = 2(4w)$$
$$48 = 8w$$
Divide both sides by 8:
$$w = \frac{48}{8} = 6$$

Step4: Find the length

Since $l = 3w$, substitute $w = 6$:
$$l = 3\times6 = 18$$

Answer:

length: 18 cm
width: 6 cm