Question

a city has a garden in the shape of an equilateral triangle with 40 feet sides. there is a walkway that runs from a gate located at the midpoint of one side of the equilateral triangle to a fountain at the opposite vertex. approximately how long is the walkway?

Answer 1

The walkway is approximately 34.64 feet long

Explanation:

The length of the sides of the equilateral triangle shaped the city garden = 40 feet

The path of the walkway = From the midpoint of a side to the opposite vertex

Therefore, we have;

Let x, represent the length of the walkway

We have that the x, a side of the equilateral triangle, and half the side of the location of the gate, forms a right triangle, with a side of the equilateral triangle representing the hypotenuse side

Therefore, we have;

40² = x² + (40/2)²

40² = x² + 20²

x² = 40² - 20² = 1200

x = √1200 = 20·√3

The length of the walkway = x = 20·√3 ≈ 34.64 feet.