Question

the length of a rectangle is twice its width. if the area of the rectangle is 50 yd², find its perimeter.

Explanation:

Step1: Let the width be $x$

Let the width of the rectangle be $x$ yards. Since the length is twice the width, the length is $2x$ yards.

Step2: Set up the area - equation

The area formula of a rectangle is $A = length\times width$. Given $A = 50$ square - yards, we have $2x\times x=50$, which simplifies to $2x^{2}=50$.

Step3: Solve for $x$

Divide both sides of the equation $2x^{2}=50$ by 2: $x^{2}=25$. Taking the square root of both sides, we get $x = 5$ (we consider the positive value since length cannot be negative).

Step4: Find the length and width

The width $x = 5$ yards, and the length $2x=10$ yards.

Step5: Calculate the perimeter

The perimeter formula of a rectangle is $P = 2(length + width)$. Substitute length = 10 yards and width = 5 yards into the formula: $P=2(10 + 5)=30$ yards.

Answer:

30 yards