The area of a rectangle is 14 yd2 , and the length of the rectangle is 3 yd less than twice the width. find the dimensions of the rectangle.

Let x be the width
2x-3= length

(2x-3)(x)=14
2x^2-3x=14
2x^2-3x-14=0
(2x- 7)(x+2)=0
x=7/2 or x=-2

Since we know that negative values cannot exist in distance, we have to take 7/2 to as the correct answer.

The width would be 3.5 yards
Length= 2(3.5)-3
=4 yards

3.5 x 4 yards is the dimension of the rectangle

Hope I helped :)

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MrRoyal MrRoyal · Answer 2 · 2022-04-20T12:21:51+02:00

The dimensions of the rectangle are 4 yd by 7/2 yd

How to determine the dimensions of the rectangle?

The area is given as:

Area = 14 yd^2

Let the width be x. So, the length is:

Length = 2x - 3

The area is then calculated as:

Area = (2x - 3) * x

Expand

Area = 2x^2 - 3x

Substitute 14 for Area

2x^2 - 3x = 14

Rewrite as:

2x^2 - 3x - 14 = 0

Factorize

(2x- 7)(x+2)=0

Solve for x

x=7/2 or x=-2

Width cannot be negative.

So, we have:

x = 7/2

Substitute x = 7/2 in Length = 2x - 3

Length = 2 * 7/2 - 3

Evaluate

Length = 4

Hence, the dimensions of the rectangle are 4 yd by 7/2 yd