Question

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Answer 1

we have,

ΔABC is an equilateral Δ with side 12 cm.
Draw AE ⊥ BC
In ΔABD and ΔACD

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ADB = ADC [ Each90 degree]

AB = AC [ each 12 cm]

AD = AD [ Common]

ABD congruent ACD [ By RHS]

using Pythagoras theorem

AD² + BD² = AB²

AD² + 6² = 12²

AD² + 36 = 144

AD² = 144.-36

AD² = 108

AD =√108

AD = 10.39 cm

Answer 2

Heya!!

Let ABC is an equilateral triangle and AD is height of this triangle stands on side BC.

Side AB = Side BC = side AC = 12 cm

Since, in equilateral triangle , BD = CD = 12/2 = 6 cm ( By RHS congruency of triangles ABD and ADC )

Now,

In triangle ADC,

AC^2 = AD^2 + CD^2

=) 12^2 = AD^2 + 6^2

=) 144 = AD^2 + 36

=) AD^2 = 144 - 36

=) AD = root 108

=) AD = 10.39 cm

Hence, the height of equilateral triangle of side 12 cm is 10.39 cm

Hope it helps uh.