Answer to Question #94407 in Geometry for Mychal

Question

I decided it is about time I portioned off a part of my yard and make a marshmallow garden. The area I have decided to portion off is created by combining two shapes: A rectangle and an equilateral triangle, with the equilateral triangle directly on top of the rectangle (think of those terrible houses you used to draw as children). I have 900 meters of fencing to use, and I know the length of the rectangular area needs to be 1.5 times the width. If the base of the triangle is the exact same in measure to the length of the rectangle, what are the dimensions of all sides of this portioned area?

Answer 1

Let the length of the rectangular area is x meters. Then

$4x+\frac{4x}{3}=900, \quad x=\frac{2700}{16}=168.75$

The length of the rectangular area is 168.75 meters. The width of the rectangular area is 112.5 meters. Base of the triangle is 112.5 meters.