Question

Find the area of a traingle whose sides are 8 cm , 15 cm and 17 cm

Answer 1

semi perimeter(s) =(a+b+c)/2

                           ( 8+15+17)/2

                             40/2

                             20 cm

herons formula =

                            $\sqrt{s(s-a)(s-b)(s-c)}\\\sqrt{20(20-8)(20-15)(20-17)}\\\sqrt{20*12*5*3}\\\sqrt{3600}$

                            60$cm^{2}$

Answer 2

$\huge{\bf{\underline{\red{Solution :}}}}$

⇒Suppose the side a = 8 cm , b = 15 cm and c = 17 cm

Now Find Semi - Perimeter :-

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

$\implies \bold{ \frac{8 + 15 + 17}{2}}$

$\implies \bold{\frac{40}{2}}$

$\implies \boxed{\bold{20 \ cm}}$

Now Find Area of Triangle by heron's Formula  :-

$\implies \boxed{\bold{Area \ of \ Triangle = \sqrt{s(s-a)(s-b)(s-c)}}}$

$\implies \bold{\sqrt{20(20 - 8)(20 - 15)(20 - 17)}}$

$\implies \bold{\sqrt{20 \times 12 \times 5 \times 3}}$

$\implies \bold{\sqrt{100 \times 36}}$

$\implies \boxed{\bold{60 \ cm^{2}}}$

Area of Triangle - 60 cm²

$\rule{200}2$

There are three types of Triangle on the basis of sides :-

1) Scalene Triangle - A triangle in which all three sides are unequal lengths is called Scalene Triangle .

2) Isosceles Triangle - A triangle in which two sides are equal lengths is called Isosceles Triangle .

3) Equilateral Triangle - A triangle in which all three sides are equal in lengths is called Equilateral triangle .