Question

The area of a rectangle is 65 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.

Answer 1

x = width
2x-3 = length 

$x(2x-3) = 65\\ 2x^2 - 3x - 65 = 0 \\ D=b^2-4ac=(-3)^2-4*2*(-65)=529\\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{3б 23}{4} \\ x_1=-5 \ \ \O \\ x_2=6.5$

width = 6.5 m
length  = 2x-3 = 2*6.5 - 3 = 10 m

Answer 2

The dimensions of the rectangle are 10 meters and 6.5 meters

Let the width of the rectangle be represented by w.

The length of the rectangle will then be:

= 2w - 3

Area of the rectangle = 65m²

Note that length × width = Area

Therefore, w × (2w - 3) = 65

2w² - 3w = 65

2w² - 3w - 65 = 0

2w² - 13w + 10w - 65 = 0

2w(w - 6.5) + 10(w - 6.5) = 0

Therefore, w - 6.5 = 0

w = 0 + 6.5

w = 6.5

Width = 6.5 meters

Length = 2w - 3

Length = 2(6.5) - 3

Length = 13 - 3

Length = 10 meters.

The dimensions of the rectangle is 10 meters and 6.5 meters

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