Calculate the area of an equilateral triangle whose height is 20 cm. Find the area of triangle whose sides are 17 cm 8 cm and 15 cm.

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40 sq. cm

50 sq. cm

60 sq. cm

70 sq. cm

answer is C.

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Detailed Solution

Given the equilateral triangle's height = 20 cm
Height and the area of an equilateral triangle ‘h’ =

\frac{h^{2}}{\sqrt{3}}

∴

Area of an equilateral triangle =

\frac{20^{2}}{\sqrt{3}}

\frac{400}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}

\frac{400 \sqrt{3}}{3}

sq. cm
Triangle with the given sides 17 cm, 8 cm 15 cm
Based on Pythagorean theorem

{(15)}^{2} + {(8)}^{2} = {(17)}^{2}

It is a triangle with a right angle.
∴ Area of triangle =

\frac{1}{2} \times b \times h

\frac{1}{2} \times 15 \times 8

= 60 sq. cm

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