Question

the length of a rectangle is twice its width. if the area of the rectangle is 50 cm², find its perimeter.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ cm. Then the length $l = 2w$ cm.

Step2: Use area formula

The area formula of a rectangle is $A=l\times w$. Substitute $l = 2w$ and $A = 50$ into it: $50=2w\times w=2w^{2}$.

Step3: Solve for width

Divide both sides of the equation $2w^{2}=50$ by 2: $w^{2}=25$. Then take the square - root of both sides. Since width cannot be negative, $w = 5$ cm.

Step4: Find the length

Since $l = 2w$, when $w = 5$ cm, $l=2\times5 = 10$ cm.

Step5: Calculate the perimeter

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 10$ cm and $w = 5$ cm into it: $P=2(10 + 5)=2\times15=30$ cm.

Answer:

30