Geomerty Problem

Question

The perimeter of a rectangle is 300 mi. If the base is 4 times the height, find the height, the base, and the area of the rectangle.

Answer 1

In this problem, we are given our perimeter which is 300 mi and a comparison of base to height. This is what we currently know:

1. Perimeter is equal to 300 mi
2. Base is 4 times the height

What we don't currently know is the value of height and since we don't know the value of height, we cannot determine the area of the rectangle.

First we must find the height of the rectangle.

The equation for the perimeter of a rectangle is 2 * length + 2 * width or 2 * (length + width)

If we allow h to stand for height, we can then substitute our known quantities in the equation and find out what the height is.

Perimeter = 2 * (base + height)

300 = 2 * (4h + h)

300 = 2 * (5h)

300 = 10h (Now we can simply solve for h)

300 / 10 = 10h / 10

30 = h

Now that we know what the height is we can determine what the base is

base = 4 * height

base = 4 * (30)

base = 120

Now that we know what the base is and the height is, we can find the area of the rectangle

area of a rectangle = base * height

A = 120 * 30

A = 3600 mi^2 (3600 square miles)

Answer 2

Let h be height

Base is 4 times height = 4h

Perimeter = 2*height + 2* base = 2*h + 2 * (4h) = 10h = 300 ---> h = 30, so base = 120

area = base * height = 30 * 120 + 360 square miles