The sum of all the three sides of an equilateral triangle is 15 \sqrt{3} {cm}. The height of the triangle is

SSC CHSL 12 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 54 of 99

Marks: +1, -0

The sum of all the three sides of an equilateral triangle is

15 √{3} {cm}

. The height of the triangle is

Solution:

Let the each side of the equilateral triangle be

x {cm}

∴ x+x+x=15 √{3}

⇒ \;\; 3 x=15 √{3}

⇒ \;\; x=\;{15 √{3}}/{3}=5 √{3} {cm}

Now, height of the triangle

\;\; =\;{√{3}}/{2} × x=\;{√{3}}/{2} × 5 √{3}

\;\; =\;{15}/{2}=7.5 {cm}

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