Question

a rectangle has an area of 120 square yards. the length is 4 more than 4 times the width. find the length and width, in yards, of the rectangle.
show your work here
length:
width:

Explanation:

Step1: Set up variables

Let the width be \( w \) yards. Then the length \( l=(4w + 4) \) yards.

Step2: Use the area formula

The area of a rectangle \( A=l\times w \). Given \( A = 120 \), so \( (4w + 4)\times w=120 \).
Expand: \( 4w^{2}+4w-120 = 0 \).
Divide by 4: \( w^{2}+w - 30=0 \).

Step3: Solve the quadratic equation

Factor \( w^{2}+w - 30=(w + 6)(w - 5)=0 \).
Set each factor equal to zero: \( w+6=0\) gives \(w=-6\) (rejected as width can't be negative), \(w - 5=0\) gives \(w = 5\).

Step4: Find the length

Substitute \(w = 5\) into \(l=4w + 4\). Then \(l=4\times5+4=24\).

Answer:

Length: \(24\) yards
Width: \(5\) yards