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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE