Question

an environmental group is making signs for an upcoming community recycling day. They want the signs to be equilateral triangles with heights of 35 in. How long in inches is each side of the signs be? Round your answer to the nearest tenth of an inch

Answer 1

This is a question for Pythagoras!

x^2 - 1/2x^2 = 35^2
1/2x^2 = 35^2
x^2 = 2(35^2)
x^2 = 2450
x = 49.49747

To the nearest tenth of an inch, the answer is 49.5

Answer 2

Hello,

If x is the hypotenus,x/2 is the half base of the triangle
so with the Pythagorean theorem, we know that:

x²=(x/2)²+35²
==>x²=x²/4 +35²
==>3x²/4=35²
==>x²=4*35² /3
==>x=2*35/√3
==>x=70/√3
==>x=40,41451884...≈40.4 (in)