Question

If a = 9 , b = 12 , c = 15 and S = and
$s = \frac{a + b + c}{2} .$
Find the values of
$\sqrt{ s(S-a)( s-b)(S-c)}$
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Answer 1

Answer:

54

Step-by-step explanation:

S = a+b+c/2

S= 9+12+15/2

S= 36/2= 18

we have,

S= 18,a= 9 ,b= 12,c= 15

Now put these values in the given formula,

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

=✓18 (18-9) (18-12) (18-15)

=✓18*9*6*3

now do the prime factorisation of all individually (18,9,6,3)

now we have,

=✓2*3*3*3*3*2*3*3

now,2*3*3*3(using prime factorisation method)

=54

Hope u get it.

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Answer 2

Heron's Formula

Heron’s formula is used to find the area of a triangle when we know the length of all its sides. It is also termed as Hero’s Formula. We don’t have to need to know the angle measurement of a triangle to calculate its area.

Area of triangle using three sides=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Semiperimeter, s= Perimeter of triangle/2 = (a+b+c)/2