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If the area of the equilateral triangle is $813 cm 2$ , its height is ____ cm.

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Detailed Solution

If the area of the equilateral triangle is

813 cm 2

, its height is 15.58 cm.
Let the sides of triangle = a.
Area of equilateral triangle is,

a r e a = 34 a 2

813 = 34 a 2 ⇒ a 2 = 81 × 4 ⇒ a 2 = 324 ⇒ a = 18 c m

Side of triangle is 18 cm.
Now, drawing a median on base and calculating height,
Question Image

B D = B C 2 ⇒ B D = 182 ⇒ B D = 9 c m

Using Pythagoras theorem in triangle ABD,

H y p o t e n u s e 2 = B a s e 2 + p e r p e n d i c u l a r 2 182 = 92 + A D 2 ⇒ A D 2 = 324 − 81 ⇒ A D 2 = 243 ⇒ A D = 93 c m

⇒

AD = 15.58 cm
The height of triangle is 15.58 cm.

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