Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The perimeter of a triangle is 30 cm and its area is $30 \mathrm{cm}^{2}$. If the largest side measures 13 cm, then what is the length of the smallest side of the triangle?
(a)3 cm
(b)4 cm
(c)5 cm
(d)6 cm
Answer
Answer (as printed): C
Explanation
Let the smallest side be $x$ cm. Then, other sides are 13 cm and $(17-x) \mathrm{cm}$. Let $a=13, b=x$ and $c=(17-x)$. So, $s=15$. $$\begin{aligned} \text { Area } & =\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{15 \times 2 \times(15-x)(x-2)}=\sqrt{30(15-x)(x-2)} \end{aligned}$$ ∴ Smallest side $=5 \mathrm{cm}$.