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Calculate the area of the triangle whose sides are $18 cm, 24 cm and 30 cm$ in length. Also find the length of the altitude corresponding to the smallest side.

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216 {cm}^{2}, 24 cm

220 {cm}^{2}, 25 cm

225 {cm}^{2}, 25 cm

168 {cm}^{2}, 25 cm

answer is A.

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Detailed Solution

Sides of given triangle,

a = 18 cm b = 24 cm c = 30 cm

By Heron's formula, triangle’s area,

A = \sqrt{s (s - a) (s - b) (s - c)}

Here,

s = \frac{a + b + c}{2}

s = \frac{18 + 24 + 30}{2} ​ = 36

Thus,

A = \sqrt{36 (36 - 18) (36 - 24) (36 - 30)} A = \sqrt{36 \times 18 \times 12 \times 6} ​ A = \sqrt{216 \times 216} ​

= 216 c m^{2}

Side, which is smallest,
a = 18 cm

Thus, area of t h e triangle

A = \frac{1}{2} ​ \times base \times altitude

216

\frac{1}{2} ​ \times 18 \times altitude

Altitude =

\frac{216}{9}

= 24 cm

Hence, the correct answer is 1.

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