Question

a rectangle has an area of 48 square yards. the length is 4 more than twice the width. find the length and width, in yards, of the rectangle.
show your work here
length:
width:

Explanation:

Step1: Define variables

Let the width be \( w \) yards. Then the length \( l=(2w + 4) \) yards.

Step2: Use the area formula

The area of a rectangle \( A=l\times w \). Substitute \( l = 2w+4 \) and \( A = 48 \):
\( (2w + 4)\times w=48 \)
Expand: \( 2w^{2}+4w-48 = 0 \)
Divide by 2: \( w^{2}+2w - 24=0 \)

Step3: Solve the quadratic equation

Factor \( w^{2}+2w - 24=(w + 6)(w - 4)=0 \)
Set each factor equal to zero: \( w+6 = 0\) gives \(w=-6\) (rejected as width cannot be negative), \(w - 4=0\) gives \(w = 4\)

Step4: Find the length

Substitute \( w = 4 \) into \( l=2w + 4 \): \( l=2\times4+4=12 \)

Answer:

length: \( 12 \)
width: \( 4 \)