An equilateral triangle has an altitude of 12 cm, find the following; a.) what is the length of each side of the triangle ? b.) what is the area of the triangle?

1 Answer
Jim G.
Dec 18, 2017

#8sqrt3" and "48sqrt3" square cm"#

Explanation:

#"the altitude of an equilateral triangle 'splits' the"#
#"triangle into 2 congruent right triangles"#

#"let the side of the equilateral triangle "=x#

#"consider one right triangle"#

#"with hypotenuse "=x#

#"and legs "=12" and "1/2x#

#"using "color(blue)"Pythagoras' theorem"#

#x^2=(1/2x)^2+12^2#

#rArrx^2=1/4x^2+144#

#rArr3/4x^2=144#

#rArrx^2=((144xx4)/3)=192#

#rArrx=sqrt192=8sqrt3larrcolor(red)"exact value"#

#"area "=1/2xx8sqrt3xx12=48sqrt3larrcolor(red)"exact value"#

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