Question

The sides of a triangle are 8 cm, 15 cm and 17 cm. Find its area.

Answer 1

Answer:

60cm^2

Explanation:

Given :

$\sf{}Sides\ of\ the\ triangle\ are\ 8 cm,15 cm\ and\ 17 cm$

To Find :

$\sf{}Area\ of\ the\ triangle =?$

Formula required :

$\sf{Heron's\; formula :-}$

$\sf{}\sqrt{(s)(s-a)(s-b)(s-c)}$

$\sf{}Here\; -:$

$\sf{}s\ is\ the\ semi\ perimeter\  and\ a,b,c\ are\ the\ sides\ of\ a\ triangle.$

Solution :

$\sf{}Perimeter\ of\ the\  triangle =a+b+c\\\\\sf{}Semi\ perimeter\ is\ the\ of\ perimeter.$

$\sf{}So,$

$\sf{}Semi\ perimeter =\dfrac{a+b+c}{2}$

$\sf{} \implies \dfrac{8+15+17}{2}\\\\\sf{} \implies \dfrac{40}{2}\\\\\sf{} \implies 20$

By Heron’s formula:-

$\sf{}\sqrt{(s)(s-a)(s-b)(s-c)}$

s - a

= 20 - 8

∴ 12cm

s - b

= 20 - 15

∴ 5cm

s - c

= 20 - 17

= 3cm

Area :-

$\sf{}\implies \sqrt{20\times12\times5\times3}$

$\sf{}\implies \sqrt{2\times2\times5\times2\times2\times3\times5\times3}$

$\sf{}\implies 2\times 5\times2\times2\times3$

$\sf \implies{}60cm^2$

Therefore, area of the given triangle is 60cm^2

Answer 2

Answer:

Answer:

60cm^2

Explanation:

Given :

\sf{}Sides\ of\ the\ triangle\ are\ 8 cm,15 cm\ and\ 17 cmSides of the triangle are 8cm,15cm and 17cm

To Find :

\sf{}Area\ of\ the\ triangle =?Area of the triangle=?

Formula required :

\sf{Heron's\; formula :-}Heron

′

sformula:−

\sf{}\sqrt{(s)(s-a)(s-b)(s-c)}

(s)(s−a)(s−b)(s−c)

\sf{}Here\; -:Here−:

\sf{}s\ is\ the\ semi\ perimeter\ and\ a,b,c\ are\ the\ sides\ of\ a\ triangle.s is the semi perimeter and a,b,c are the sides of a triangle.

Solution :

\begin{gathered}\sf{}Perimeter\ of\ the\ triangle =a+b+c\\\\\sf{}Semi\ perimeter\ is\ the\ of\ perimeter.\end{gathered}

Perimeter of the triangle=a+b+c

Semi perimeter is the of perimeter.

\sf{}So,So,

\sf{}Semi\ perimeter =\dfrac{a+b+c}{2}Semi perimeter=

2

a+b+c

\begin{gathered}\sf{} \implies \dfrac{8+15+17}{2}\\\\\sf{} \implies \dfrac{40}{2}\\\\\sf{} \implies 20\end{gathered}

⟹

2

8+15+17

⟹

2

40

⟹20

By Heron’s formula:-

\sf{}\sqrt{(s)(s-a)(s-b)(s-c)}

(s)(s−a)(s−b)(s−c)

s - a

= 20 - 8

∴ 12cm

s - b

= 20 - 15

∴ 5cm

s - c

= 20 - 17

= 3cm

Area :-

\sf{}\implies \sqrt{20\times12\times5\times3}⟹

20×12×5×3

\sf{}\implies \sqrt{2\times2\times5\times2\times2\times3\times5\times3}⟹

2×2×5×2×2×3×5×3

\sf{}\implies 2\times 5\times2\times2\times3⟹2×5×2×2×3

\sf \implies{}60cm^2⟹60cm

2

Therefore, area of the given triangle is 60cm^2