Question

Height of the equilateral triangle with side 12cm is
A) 6,5 cm
B) 12V3 cm
0 24 cm
Di 12cm​

Answer 1

Answer:

Let ABC be the equilateral triangle with AD as an altitude from A meeting BC at D. Then, D will be the midpoint of BC. Applying Pythagoras theorem in right-angled triangle ABD, we get: Hence, the height of the given triangle is 6√3 cm.

Answer 2

Given:-

•Side of an equilateral triangle is 12cm.

To Find:-

•Height of an equilateral triangle.

Solution:-

Altitude of an equilateral triangle bisects into two sides and forms right angled triangles with the remaining sides.

So,CD=DB=6cm

Also in △ADC,∠ADC=90∘

Now apply pythagoras theorem gives

$\: \: \sf \: {(ac)}^{2} = {(cd)}^{2} + {(ad)}^{2}$

Now substiute the values,

$\: \: \sf \: {(12)}^{2} = {(6)}^{2} + {(ad)}^{2} \\ \\ \: \: \sf \: 144 = 36 + {(ad)}^{2} \\ \\ \: \: \sf \: {(ad)}^{2} = 108 \\ \\ \: \: \sf \: ad = \sqrt{108} = 6 \sqrt{3} ccm$

Therefore,the height of equilateral triangle is 6√3cm.

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