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If the Altitude of an Equilateral Triangle is 2 cm shorter than its side, Find the Length of its side.

Sagot :

If x is the side of the triangle then its altitude should be [tex] \frac{ \sqrt{3} }{2} x[/tex] (from the property of 30-60-90 triangle)

Altitude: x-2  (is 2 cm shorter than its side)

[tex]x-2= \frac{ \sqrt{3} }{2}x \\ \\ 2x-4= \sqrt{3}x \\ \\ (2- \sqrt{3})x=4 \\ \\ x= \frac{4}{2-\sqrt{3} }=\boxed{8+4 \sqrt{3}} [/tex]


Length of side = [tex]8+4 \sqrt{3}[/tex] cm

the answer is   8+4 \sqrt{3] cm