Question

A rope is cut so that one piece is three times the length

of the other. Each rope is then used to enclose an area
in the shape of an equilateral triangle. If the area
enclosed by the shorter rope is 1,000 m2, what is the
area enclosed by the longer rope?

Answer 1

9,000 m2

Explanation:

If the longer rope has three times the length of the shorter rope, the perimeter and the sides of the triangle formed by the longer rope are three times the perimeter and sides of the triangle formed by the smaller rope.

The area of an equilateral triangle is:

`Area = (side^(2) * √(3))/(4)`

So, if the side is three times bigger, the area will be 9 times bigger (3^2).

The area of the small triangle is 1000 m2, so the area of the bigger triangle is 9 * 1,000 = 9,000 m2