Question

the length of a rectangle is twice its width. if the perimeter of the rectangle is 42 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 $l = 2w$ cm.

Step2: Write the perimeter formula

The perimeter $P$ of a rectangle is $P=2(l + w)$. Substitute $l = 2w$ and $P = 42$ into the formula: $42=2(2w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $2(2w + w)=2\times3w=6w$. So the equation becomes $6w = 42$.

Step4: Solve for $w$

Divide both sides of the equation $6w = 42$ by 6: $w=\frac{42}{6}=7$ cm.

Step5: Solve for $l$

Since $l = 2w$, substitute $w = 7$ into the equation: $l=2\times7 = 14$ cm.

Answer:

length: 14 cm
width: 7 cm