What is the base length of an equilateral triangle that has an area of approx 9.1 square centimeters?

1 Answer
Dec 1, 2015

#~~4.58# #cm#

Explanation:

jwilson.coe.uga.edu

We can see that if we split an equilateral triangle in half, we are left with two congruent equilateral triangles. Thus, one of the legs of the triangle is #1/2s#, and the hypotenuse is #s#. We can use the Pythagorean Theorem or the properties of #30˚-60˚-90˚# triangles to determine that the height of the triangle is #sqrt3/2s#.

If we want to determine the area of the entire triangle, we know that #A=1/2bh#. We also know that the base is #s# and the height is #sqrt3/2s#, so we can plug those in to the area equation to see the following for an equilateral triangle:

#A=1/2bh=>1/2(s)(sqrt3/2s)=(s^2sqrt3)/4#

We know that the area of your equilateral triangle is #9.1#.

We can set our area equation equal to #9.1#:

#9.1=(s^2sqrt3)/4#

#36.4=s^2sqrt3#

#s^2~~21.02#

#s~~4.58# #cm#