Question

linear equations
finding the dimensions of a rectangle given its perimeter and a...
the length of a rectangle is twice its width.
if the perimeter of the rectangle is 30 ft, find its length and width.
length: ft
width: ft

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) ft. Then the length \( l \) is \( 2w \) ft (since length is twice the width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 30 \) ft, so substitute \( l = 2w \) into the formula:

$$ 30 = 2(2w + w) $$

Step3: Simplify and solve for \( w \)

Simplify the right - hand side: \( 2(2w + w)=2(3w) = 6w \). So the equation becomes \( 30 = 6w \). Divide both sides by 6: \( w=\frac{30}{6}=5 \) ft.

Step4: Find the length

Since \( l = 2w \), substitute \( w = 5 \) into this formula: \( l = 2\times5 = 10 \) ft.

Answer:

length: \( 10 \) ft
width: \( 5 \) ft