Question

Find the area of the triangle whose sides are 13cm 20 cm and 21cm. Also find the height of the triangle corresponding to the largest side.

Answer 1

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Answer 2

Answer :-

Step by step explanation :-

Area of ∆ :

Here find area from heron's formula :-

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

$= \frac{13 + 20 + 21}{2} = 27$

$= \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{27 \times 14 \times 7 \times 6} \\ = \boxed{126 {cm}^{2} }$

Height :-

Here longest side{base} is 21cm.

We know that

area of triangle = $\frac{1}{2}×base×height$

area of triangle = ${126cm}^{2}$

Compare :-

$126 = \frac{1}{2} \times 21 \times h \\ \\ 126 \times 2 = 21h \\ \\ h = 12.09cm = \boxed{12cm}$

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