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The perimeter of a triangle with sides of integer values is equal to 13. How many such triangles are possible?
Answer & Solution
Correct Answer:
Option
A
Number of possible triangles when perimeter is odd
$$\eqalign{ & = \frac{{{{\left( {P + 3} \right)}^2}}}{{48}} \cr & = \frac{{{{\left( {13 + 3} \right)}^2}}}{{48}} \cr & = \frac{{16 \times 16}}{{48}} \cr & = \frac{{16}}{3} \cr & = 5\,... \cr & = 5 \cr} $$
$$\eqalign{ & = \frac{{{{\left( {P + 3} \right)}^2}}}{{48}} \cr & = \frac{{{{\left( {13 + 3} \right)}^2}}}{{48}} \cr & = \frac{{16 \times 16}}{{48}} \cr & = \frac{{16}}{3} \cr & = 5\,... \cr & = 5 \cr} $$
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