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The height of an equilateral triangle is...

The height of an equilateral triangle is 15 cm. The area of the triangle is

A

`50sqrt3 cm^2`/ `50sqrt3` वर्ग सेमी

B

`70sqrt3 cm^2`/ `70sqrt3` वर्ग सेमी

C

`75sqrt3 cm^2`/ `75sqrt3` वर्ग सेमी

D

`150sqrt3 cm^2`/ `150sqrt3` वर्ग सेमी

Text Solution

Verified by Experts

The correct Answer is:
C
माना कि समबाहु त्रिभुज की भुजा x है।
`:.` समबाहु त्रिभुज की ऊँचाई `=(sqrt3)/(2)xx` भुजा
`implies(sqrt3)/(2)x=15`
`impliesx=2xx5sqrt3=10sqrt3`
`:.` क्षेत्रफल `=(sqrt3)/(4)xx("भुजा")^(2)=(sqrt3)/(4)xx10sqrt3`
`=(sqrt3)/(4)xx300`
`=75sqrt3cm^(2)`
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