Question

. The sides of a triangle are in the ratio 3 : 6 : 4. If its semi-perimeter is 52 cm, its
shortest side is :
a) 24 cm b) 30 cm

c) 50 cm d) NOTA​

Answer 1

To find : shortest side of triangle .

Given : sides of a triangle are in the ratio $3 : 6 : 4$ .Its semi-perimeter is $52$ cm.

Solution :

• As per given data we know that sides of a triangle are in the ratio $3 : 6 : 4$ .Its semi-perimeter is $52$ cm. We have to find shortest side of triangle .
• Let , $3x , 6x , 4x$ be the sides of triangle.
• We know that, perimeter of triangle is sum of three side of triangle.
• If $\mathrm{a}, \mathrm{b}, \mathrm{c}$  are the sides of triangle then,
• Perimeter of triangle $=a+b+c$
• Semi -perimeter = $\frac{Perimeter}{2}$
• Therefore , substituting the values in above formula we get ,

       $52 = \frac{3x + 6x + 4x}{2} \\52 = \frac{13x }{2} \\104 = 13x \\ x =\frac{104}{13} \\ x= 8$

• Now , substituting the value of $x$ in sides to find original sides .

       $3x = 3\times 8 = 24\ cm \\6x = 6\times = 6\times 8 = 48\ cm \\4x = 4\times 8 = 32\ cm$  

• $24$ cm is the shortest side of triangle .

Hence ,shortest side is $24$ cm .Therefore , option a) $24$ cm is correct .