An equilateral triangle has sides of length 15 cm?

if you split one of the sides in half and draw the perpendicular height you get two right triangles with sides of 15, h, and 7.5 where 15 is the hypotenuse.

use the pythagorean theorem

15^2 = 7.5^2 + h^2

solve for h

h = sqrt(225 - 56.25) = 12.990 cm

Draw the perpendicular and you'll end up with a 30, 60, 90 triangle where the hypotenuse = 15 cm. This means the short side = 1/2 hypotenuse = 15/2 cm and the long side (which is the height) = 15√3/2 cm

Height of triangle = = 15√3/2 cm

I'm guessing 15.6cm^2 is the area. Before we begin, remember that all the angles in an equilateral triange equals 60 degrees and that all the sides are equal. The area of a triangle is 1/2 bh. Let the base (b) equal s, which is the lenght of one of the sides. To find the height, split the triangle in half and you get two special 30-60-90 right triangles. Remember the proportion of the sides in a 30-60-90 is x:x(sqrt3):2x The side opposite of the 30 degrees angle is s/2, since you split the original triangle in half. Then the height of the original triangle AKA the side opposite the 60 degrees angle is s(sqrt3) / 2 Back to the area of the original triangle... A=1/2 bh A=15.6 b=s h=s(sqrt3) / 2 1/2 bh = 1/2 s * s(sqrt3)/2 =1/4 (s^2 ) (sqrt3) = 15.6 SOLVE for s. (Divide both sides by 1/4) (s^2 ) (sqrt3) = 62.4 (Divide both sides by sqrt3) s^2 = approx. 36.02666 s=sqrt(36.02666) s= approx. 6.0022 cm <--ANSWER P.S. I'm not sure how many digits you want to round to. FOR FUTURE REF: Area of an equilateral triange = (sqrt3) /4 (s^2) ...where s=length of one side Hope that helps! I know it seems a bit long, but I just like to space things out.

The height forms the longer leg of a 30-60-90 triangle. In a 30-60-90 triangle, take the shorter leg, in this case 15/2 = 7.5 and multiply it by the sqrt of 3. In this case 7.5 x sqrt 3 = 12.99 ~13

first draw a perpendicular line from one angleto the opposite side, splitting the side in half.

use pythagorean theorem a^2+b^2=c^2. the a^2 wouldbe half of the bottom line because the perpendicular height would split the bottom line in half. b^2 is what youre looking for. and c^2 is the side(diagonal) which would equal 15. so use the eqaution and solve for b and find b=8.2915

height = (1/2)(side)(√3) = 13