Verified answer

The rectangle has a width of 2 in and a length of 10 in.

Step-by-step explanation:

Step 1: Identify the given values

l = 3w + 4

A = 20

Step 2: Formulate an equation using the formula for the areaof the rectangle.

The area of a rectangle is given by the equation:

A = l x w

where: A - area

l - length

w - width

Substitute the value of A which is 20 in the equation

20 = l x w

Step 3: Solve for width and length

Substitute the value of l and A

20 = (3w + 4)(w)

20 = 3w² + 4w

3w² + 4w - 20 = 0

Factor the equation

(3w + 10)(w - 2) = 0

w1 = -10/3 | w2 = 2

Considering that width can't be negative, width = 2 in

Solve for l

l = 3w + 4

l = (3)2 + 4

l = 10 in

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