Question

Find the area of the triangle whose sides are $17cm,25cm,26cm$

Answer 1

Step 1:Finding the semi perimeter of the triangle :

Given sides of the triangle are $17cm,25cm,26cm$

Since the triangle is a scalene triangle,

Area of the scalene triangle = $\sqrt{s(s-a)(s-b)(s-c)}\mathrm{where}\mathrm{a},\mathrm{b},\mathrm{c}\mathrm{are}\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{triangle}\mathrm{and}\mathrm{s}\mathrm{is}\mathrm{the}\mathrm{semiperimeter}.$

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

$$\begin{gathered} s=\frac{17+25+26}{2} \\ =\frac{68}{2} \\ =34cm. \end{gathered}$$

Step 2 Finding the area of the triangle:

$$\begin{gathered} s-a=34-17=17cm \\ s-b=34-25=9cm \\ s-c=34-26=8cm \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{34\times 17\times 9\times 8} \\ =\sqrt{17\times 2\times 17\times 3\times 3\times 2\times 4} \\ =17\times 2\times 2\times 3 \\ =204c{m}^2. \end{gathered}$$

Hence the area of the triangle is $204c{m}^2.$