The area of an equilateral triangle is 173.2 metre square. Find its perimeter.
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Answer:
The area of any triangle is half the base length multiplied by the vertical height to the opposite peak from that base. If the triangle is equilateral, it has three equal angles as well as the three equal sides. There are 180 degrees inside every triangle, so the angles inside are each 60 degrees. Splitting the peak angle vertically above the base results in two triangles having 30 degrees, 60 degrees and 90 degrees respectively at the corners. A 30/60/90 triangle has side lengths of 1 unit (short side), 2 units (hypotenuse), and 1.732 units (third side). If each side is of length A units, the area is then given by the formula Area =[ (A/2) * 1.732 (A/2)] = (1.732 A^2)/4. Rearranging, we get that A^2 = 172.2 * 4/1.732. Therefore A = sq rt[ 688.8/1.732] = 19.942 units and a perimeter of 59.827. Maybe the questioner was trying to say the area was 173.2, which would then result in a side length of exactly 20 and a perimeter of 60 units? Hint: the sq rt of three is 1.732, something I learned in primary school….
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