An equilateral triangle has an area of 100 cm2 What is the length of a side?

Answer 1

Call the unknown length 2l. Draw a perpendicular bisector of one side through the opposite vertex. This creates two right triangles with sides of 2l, l, and, from the Pythagorean theorem, (l X sq rt 3). The latter of these is the altitude of the triangle, and its base is 2l. The area of any triangle equals one-half the product of the base and the altitude, which in this instance is (sq rt 3) X l2. This area is stated to be 100 cm2, so that l2 = 100/(sq rt 3) = about 57.7; l = about 7.598 cm, and the side length = 15.2 cm, to the justified number of significant digits.