Question

Q-The sides of a triangle are 12cm,35cm and 37 cm.Find its area.

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Answer 1

Hi..

a=12 cm
b= 35cm
c= 37cm

$s = \frac{ a+ b + c}{2}$
$s = \frac{12 + 35 + 37}{2}$

$s = 42cm$

$area = \sqrt{s(s - a)(s - b)(s - c)}$
$= \sqrt{42(42 - 12)(42 - 35)(42 - 37)}$
$= \sqrt{42 \times 30 \times \times 7 \times 5}$
$\sqrt{2 \times 3 \times 7 \times 5 \times 2 \times 3 \times 7 \times 5}$
$= 2 \times 3 \times 7 \times 5$

${ \bold{area = 210 {cm}^{2} }}$

#THANKS

Answer 2

Answer: 210 sq. cm

Step-by-step explanation:

Heron's Formula :

$\bold{= \sqrt{ s(s-a)(s-b)(s-c)}} \\ \\ \bold{Where\: s= \frac{a+b+c}{2} = \frac{12+35+37}{2} cm} \\ \\ \bold{ s = 42\:cm} \\ \\ \bold{ = \sqrt{42(42-12)(42-35)(42-37)}} \\ \\ \bold{= \sqrt{2\times3\times7\times2\times3\times5\times7\times5}} \\ \\ \bold{= 2\times3\times7\times5\:cm^2 = 210\:cm^2}$

Concept :

Take the factors of term and we must remeber that when same term cones twice then we take one of them out due to root. Remember that s is none other than a semi perimeter.