Question

find the dimensions of a rectangle whose width is 5 miles less than its length and whose area is 66 square miles

Answer 1

A = l * w
66 = l * (l - 5)
66 = $l^{2}$-5l
0 = $l^{2}$-5l - 66

l = 11 or 6 check which works.

A = 11 * 6, which fits.

length = 11 miles
width = 5 miles

Answer 2

The dimensions of a rectangle whose width is 5 miles less than its length and whose area is 66 square miles will be 11 miles and 6 miles.

What is the area of the rectangle?

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We have to find the dimensions of a rectangle whose width is 5 miles less than its length and whose area is 66 square miles.

Let consider the width of rectangle = x

The length of rectangle = x-5

The area of the rectangle = length × Width

A = l x w

66 = x(x- 5)

66=x^2-5x

x^2-11x+6x-66=0

x(x-11)+6(x-11)=0

(x+6)(x-11)=0

x=-6,11

here x = 11 is acceptable

The length of rectangle = x-5 = 11-5 = 6cm

The length = 6 miles

The width = 11 miles

Hence, the dimensions of a rectangle whose width is 5 miles less than its length and whose area is 66 square miles will be 11 miles and 6 miles.

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