Question

a rectangles length and width are in a ratio of 5:4. the perimeter is 54 yards. what are the length and width? length = yards width = yards

Explanation:

Step1: Set up variables

Let the length be \(5x\) yards and the width be \(4x\) yards.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P = 2(l + w)\). Substituting \(l = 5x\), \(w = 4x\), and \(P=54\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Divide both sides of the equation \(54 = 18x\) by \(18\):

$$x=\frac{54}{18}=3$$

Step4: Find length and width

Length \(l = 5x\), substituting \(x = 3\), \(l=5\times3 = 15\) yards.
Width \(w = 4x\), substituting \(x = 3\), \(w=4\times3 = 12\) yards.

Answer:

length = \(15\) yards, width = \(12\) yards