Question

find the area of the triangle using heron's formula for the given sides 8 cm 5 cm and 13 cm​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :- }}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• Sides of triangle are - 8cm , 5cm , 13cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Area of triangle using herons formula

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

: ➜ $\sf \sqrt {s(s - a)(s - b)(s - c) }$ ----------- (1)

$\:\:$

Where,

$\:\:$

• a = First side

• b = Second side

• c = Third side

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

$\:\:$

Given in the question

$\:\:$

• a = 8 cm

• b = 5 cm

• c = 13 cm

• s = $\sf \dfrac {8 + 5 + 13 }{2 } = \dfrac {26 }{2 } = 13$

$\:\:$

Putting the above values in (1)

$\:\:$

: ➜ $\sf \sqrt {13(13 - 8)(13 - 5)(13 - 13) }$

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: ➜ $\sf \sqrt {13(5)(8)(0) }$

$\:\:$

: : ➨ 0

$\:\:$

• Hence the area of given triangle is 0 sq. cm i.e the triangle is not possible

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :- }}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• Sides of triangle are - 8cm , 5cm , 13cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Area of triangle using herons formula

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

: ➜ $\sf \sqrt {s(s - a)(s - b)(s - c) }$ ----------- (1)

$\:\:$

Where,

$\:\:$

a = First side

b = Second side

c = Third side

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

$\:\:$

Given in the question

$\:\:$

a = 8 cm

b = 5 cm

c = 13 cm

s = $\sf \dfrac {8 + 5 + 13 }{2 } = \dfrac {26 }{2 } = 13$

$\:\:$

Putting the above values in (1)

$\:\:$

: ➜ $\sf \sqrt {13(13 - 8)(13 - 5)(13 - 13) }$

$\:\:$

: ➜ $\sf \sqrt {13(5)(8)(0) }$

$\:\:$

: : ➨ 0

$\:\:$

Hence the area of given triangle is 0 sq. cm i.e the triangle is not possible