Question

find the area the height of a equilateral triangle whose each side measure: I) 12 cmii) 10 m iii) 6.4 m (take √3=1.73 in each side)

Answer 1

Solution: Let the side of the equilateral triangle ABC be a

If we construct a median AM at BC.

Then triangle in triangle AMB

AC=a  , BM=1/2AB =1/2a,then by Pythagoras theorem .

$AB^2=AM^2+BM^2\\\Rightarrow\ a^2=AM^2+(\frac{1}{2a})^2\\\Rightarrow\ AM^2=a^2-(\frac{1}{2a})^2=\frac{3}{4}a^2\Rightarrow\ AM=\sqrt{3}/4a=0.865a$

where AM is the height of the triangle.

1) Side of a equilateral a = 12 cm

Then height of equilateral triangle=0.865×12=10.38 cm

2)Side of a equilateral a = 10 cm

Then height of equilateral triangle=0.865×10= 8.65 cm

3)Side of a equilateral a = 6.4 cm

Then height of equilateral triangle=0.865×6.4=5.536 cm