# Find Smallest Side of Triangle if Perimeter and Area is Given

The perimeter of a triangle is 30 cm and its area is 30 cm^{2}. If the length of the largest side of the triangle is 13 cm, then what is the smallest side of the triangle?

- 5 cm
- 6 cm
- 4 cm
- 3 cm

**Answer: (1) 5 cm**

**Explanation:-
**The perimeter of a triangle = 30 cm

the area of a triangle = 30 cm

^{2}

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 + b^{2} = 17 b

b^{2} – 17 b + 60 = 0

b^{2} – 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.