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?

The walkway is approximately 34.64 feet long

Step-by-step 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.

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752