Question

This question is based on Heron's Formula :

In a triangle ABC, it is given that (s - a) = 5, (s - b) = 3, (s - c) = 1 where s is the semi perimeter and a, b, c are the sides of the triangle. If the area of the triangle is 3sqrt10 sq. units then the perimeter of the triangle is what???

Answer 1

first, write down Heron's formula

Answer 2

\[Area = \sqrt{s(s-a)(s-b)(s-c)}\]

Answer 3

now fill in what you know (from the question)

Answer 4

I substituted vales and found s=6 but it does not work ......

Answer 5

s= is (a+b+c)/2
a+b+c is the perimeter
you want 2*s for the answer

Answer 6

I have already tried by substituting values and got s=6 but it is not correct

Answer 7

Options for answer are:
a) sqrt15
b) 9
c) 27
d) 18

Answer 8

in that case you are the victim of a typo, because the perimeter is 12

Answer 9

but if you take s=6 and find values of a, b and c and then find s by a+b+c/2, you get a different value of s

Answer 10

even worse, we find a=1, b= 3 and c= 5
and that cannot be a triangle. (c must be less than 4 to be a triangle)

Answer 11

Right!! I was wondering whether I was wrong in my process or was there a mistake in the question itself.........

Answer 12

there is something wrong with the question, as it poses an impossible situation
I assume there is a typo in the original givens, but it is difficult (for me) to guess what they really meant.

Answer 13

Thanks anyway for your help.....

Answer 14

You can ask your teacher about this one (if you have a teacher).

Answer 15

This question is from last year's paper of some other school.......