Question

The length of a rectangle is three times as long as its width. The width of this rectangle is 6 inches smaller than its length. Find the length and the width. (It would also be interesting to know its area and perimeter!)

Answer 1

The length is 9in and the width is 3in

The perimeter is 24in and the area is 27in²

Explanation:

To start we have to make 2 equations with the information that gave us the problem

l = length

w = width

w = l - 6in

l = 3w

we replace l in the first equation with (3w)

w = (3w) - 6in

w - 3w = -6in

-2w = -6in

w = -6in / (-2)

w = 3in

now we replace the value of w in the second equation

l = 3w

l = 3 (3in)

l = 9in

Now that we have the length and width we can calculate the perimeter and the area with the following formulas

p = perimeter

a = area

p = 2w + 2h

p = 2(3in) + 2(9in)

p = 6in + 18in

p = 24in

a = w * l

a = 3in * 9in

a = 27in²