CTET 2 Math and Science 2011 Paper

Question : 49 of 120

Marks: +1, -0

The ratio of the side and height of an equilateral triangle is

Solution:

Let ABC be an equilateral triangle of side 'a' and height h.
So, area of 'ABC = Area of ΔABD + Area of ΔADC

\;\;{√{3}}/{4}a^{2}=\;\;{1}/{2}×\;\;{a}/{2}×h+\;\;{1}/{2}×\;\;{a}/{2}×h

\;\;{√{3}}/{4}a^{2}=\;\;{2ah}/{4}=\;\;{ah}/{2}

⇒\;\;{√{3}}/{4}a=\;\;{h}/{2}⇒\;\;{√{3a}}/{2}=h⇒\;\;{a}/{h}=\;\;{2}/{√{3}}

Hence, Required ratio

=2:√3

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