The area of a rectangle is 65ft^2 and the length of the rectangle is 3ft less than twice the width. Find the dimension of the rectangle

Answer 1

Length = 10 feet

Width = 6.5 feet

Area of a rectangle = Length x Width

A = lw

A = 65

l = 2w - 3

A = (2w -3)w

65 = 2w² - 3w

We can set up a quadratic equation by subtracting 65 from both sides of the equation

0 = 2w² - 3w - 65

Factoring

0 = (2w - 13)(w + 5)

w = 13/2, 6 1/2, feet because this dimension cannot be negative

w = 6.5 feet

l = 2w -3 = 2(13/2) - 3 = 13 - 3 = 10

Checking with the area

A = lw

65 = 10(13/2)

65 = 5(13)

65 = 65

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