Question

Find the area of a triangle whose sides are 18
cm, 24 cm and 30 cm.
Also, find the length of altitude corresponding
to the largest side of the triangle.
how is 30 a base​

Answer 1

Answer

Area of triangle = 216 cm²

Length of the altitude corresponding to the largest side of the triangle is 14.4 cm

Given

Sides of a triangle are 18 cm , 24 cm , 30 cm respectively .

To Find

Area of a triangle

Length of altitude of triangle corresponding to largest side

Formula Used

$\bullet \;\; \rm Heron's\ Formula\\\\\bullet \;\; \rm \sqrt{s(s-a)(s-b)(s-c)}\\\\\rm where,s\ denotes\ semiperimeter\\\\\to\ \rm s=\dfrac{a+b+c}{2}\\\\\bullet \;\; \rm Area\ of\ \Delta\ =\dfrac{1}{2}\times base\ \times height$

Solution

Let ,

a = 18 cm

b = 24 cm

c = 30 cm

$\rm \to\ Semi-perimeter,s=\dfrac{a+b+c}{2}\\\\\rm \to\ s=\dfrac{18+24+30}{2}\\\\\rm \to\ s=\dfrac{72}{2}\\\\\rm \to\ s=36\ cm$

Now , apply Heron's formula ,

$\to \rm \sqrt{s(s-a)(s-b)(s-c)}\\\\\to \rm \sqrt{36(36-18)(36-24)(36-30)}\\\\\to \rm \sqrt{36(18)(12)(6)}\\\\\to \rm \sqrt{36\times 9\times 2\times 4\times 3\times 3\times 2}\\\\\to \rm 6\times 3\times 2\times 2\times 3\\\\\to \rm 216$

So , Area of triangle is 216 cm²

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Now , we need to find length of altitude corresponding to the largest side of the triangle .

So , Base of the triangle is 30 cm

⇒ Base , b = 30 cm

Height , h = ? cm

Area of the triangle , A = 216 cm²

Apply formula for triangle ,

$\to \rm A=\dfrac{1}{2}\times b\times h\\\\\to \rm 216=\dfrac{1}{2}\times 30\times h\\\\\to \rm 216=15\times h\\\\\to \rm h=14.4\ cm$

So , length of the altitude corresponding to the largest side of the triangle is 14.4 cm .

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