An equilateral triangle has sides with length #x# cm. The area of the triangle is 36cm². What is the value of x? Give the answer correct to 3 significant figures.

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Answer 1 · 2016-06-13T15:37:02

#9.12# to 3 sf

The area of a triangle can be found using the TRig area rule:
#Area = 1/2"abSinC"#

As this is an equilateral triangle, all the sides are #x# and all the angles are 60°.

#1/2 (x)(x) Sin60 = 36#
#x^2 sqrt3/2 = 36 xx 2#

#x^2 = (36 xx 4)/sqrt3#

#x = 9.118 rArr 9.12# to 3 sf