Question

Suppose the length of a certain rectangle is 6 meters less than four times its width. The perimeter of the rectangle is 78 meters. Find the length and width of the rectangle.

Answer 1

Let's start by using the formula for the perimeter of a rectangle, which is:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

We're given that the perimeter is 78 meters, so we can write:

78 = 2L + 2W

Simplifying this equation, we get:

39 = L + W

We're also given that the length is 6 meters less than four times the width, so we can write:

L = 4W - 6

Now we can substitute this expression for L into the equation we got earlier:

39 = (4W - 6) + W

Simplifying this equation, we get:

39 = 5W - 6

Adding 6 to both sides, we get:

45 = 5W

Dividing both sides by 5, we get:

W = 9

So the width of the rectangle is 9 meters. We can use this value to find the length:

L = 4W - 6 = 4(9) - 6 = 30

So the length of the rectangle is 30 meters.