question_answer

The perimeter of a triangle is 40 cm and its area is \[60\,\,c{{m}^{2}}.\]If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is

A) 4

B)  6      

C)  8

D)  15

Correct Answer: C

Solution :

Let all sides of a triangle be a,b and c.

\[\therefore \]      \[a+b+c=40\]

\[\Rightarrow \]   \[a+b=40-17\]               \[(\because c=17\,\,cm)\]

\[\Rightarrow \]   \[a+b=23\]                                ?(i)

\[\therefore \]Semiperimeter of triangle

\[(s)=\frac{a+b+c}{2}=\frac{40}{2}=20\,\,\text{cm}\]

\[\therefore \]      Area of triangle \[=\sqrt{s\,\,(s-a)(s-b)(s-c)}\]

\[\Rightarrow \]               \[60=\sqrt{20\,\,(20-a)(20-b)\times 3}\]

x

[from Eq.(i)]

Again,

?(ii)

On solving Eqs. (i) and (ii), we get

Hence, the smallest side is 8 cm.