Question

Find the dimensions of a rectangle whose width is 6 miles less than it’s length and whose are is 55 square miles.

Answer 1

Hey there!!

How do we find the area of a rectangle?

Length * Breadth = Area

... Length * breadth = 55

Width is 6 miles less than the length.

... Width = Length - 6

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... Length ( Length - 6 ) = 55

... Length² - 6Length = 55

... Length² - 6Length - 55 = 0

... Length² + 5Length - 11Length - 55 = 0

... Length ( Length + 5 ) - 11 ( Length + 5 ) = 0

... ( Length - 11 ) ( Length + 5 ) = 0

... We could find two solution.

They are : 11 and -5.

As the values can not be in negatives, the appropriate length would be '11'

Length = 11

Breadth = Length - 6

... Breadth = 11 - 6

... Breadth = 5

Hence, the Length = 11 and the Breadth = 5

Hope my answer helps!

Answer 2

area = width * length

or

A = W * L

55 = W * (W+6)

solve for width:

0 = W^2 + 6W - 55

this is a quadratic and has two solutions -11 and 5

a length can only be non-negative so discard -11.

width W = 5 miles

now the length is 5+6 = 11 miles