Question

5 cm , 12 cm, 13 cm sopve with herons formula and the area of a triangle

Answer 1

Given, the sides of a triangle are = 5cm, 12cm and 13cm

Semi-perimeter = (a + b + c) / 2

s = (5 + 12 + 13) / 2

s = 30/2

s = 15cm

Area of the triangle (According to the Heron's Formula)

$= \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ \\ = \sqrt{15(10)(3)(2)} \\ \\ = \sqrt{900} \\ \\ = 30 {cm}^{2}$

Answer 2

$\textcolor{blue}{herons \: \: formula \: = \sqrt{s(s - a)(s - b)(s - c)} }$

s = semi perimeter
a, b, c = sides,



On applying formula, we get,


Semi perimeter = ( 5 + 12 + 13 ) /2
Semi perimeter = 15 cm


$\fcolorbox{red}{aqua}{area} = \sqrt{15(15 - 5)(15 - 13) (15 - 12)} \\ \\ \\ = > \fcolorbox{blue}{aqua}{area} = \sqrt{15 \times 10 \times 2 \times 3} \\ \\ \\ => \fcolorbox{blue}{aqua}{area} = \sqrt{3 \times 5 \times 2 \times 5 \times 2 \times 3} \\ \\ \\ => \fcolorbox{blue}{aqua}{area} = 3 \times 5\times 2 \: \: {cm}^{2}$


Hence, Area = 30 cm²