Find Smallest Side of Triangle if Perimeter and Area is Given
The perimeter of a triangle is 30 cm and its area is 30 cm2. 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 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.
