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 $x$ cm. Then the length is $3x$ cm.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$. Substitute $l = 3x$, $w=x$ and $P = 48$ into the formula: $48=2(3x + x)$.

Step3: Simplify the equation

First simplify the right - hand side: $2(3x + x)=2\times4x = 8x$. So the equation becomes $8x=48$.

Step4: Solve for $x$

Divide both sides of the equation $8x = 48$ by 8: $x=\frac{48}{8}=6$.

Step5: Find length and width

The width $w=x = 6$ cm. The length $l = 3x=3\times6 = 18$ cm.

Answer:

length: 18 cm
width: 6 cm