Find Smallest Side of Triangle if Perimeter and Area is Given

Answer: (1) 5 cm

Explanation:-
The perimeter of a triangle = 30 cm
the area of a triangle = 30 cm²
Then, ab/2 = 30
ab = 30 x 2
ab = 60 cm
a = 60/b

The  a  + b + 13 = 30
a + b = 30 – 13
a + b = 17          ………….. (1)
Put the value of a = 60/b in equation (1),
60/b + b = 17
60 + b² = 17 b
b² – 17 b + 60 = 0
b² – 12b – 5 b+ 60
b (b – 12) – 5 (b – 12) = 0
(b – 12) (b – 5) = 0
b – 12 = 0 & b – 5 = 0
b = 12 and b = 5

Then, the sides of the triangle are 5, 7 and 13.

Then, the smallest side of the triangle is 5.

Hence, the answer is (1) 5 cm.