Q26 / 52 · KVPY 2017 (19 Nov SA) · Mathematics

Consider four triangles having sides $(5,12,9),(5,12,11),(5,12,13)$ and $(5,12,15)$. Among these, the triangle having maximum areahas sides

A
$(5,12,9)$
B
$(5,12,11)$
Correct answer
C
$(5,12,13)$
D
$(5,12,15)$

Solution

Clearly area of $\Delta$ having sides $(5,12,13)$ is greatest (use $\Delta=\sqrt{s(s-a)(s-b)(s-c)}$

Hence, the correct answer is option: 'C'.

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