Question

The perimeter of a triangle is 10 cm. If one of the sides is 4 cm. What are the other two sides of the triangle for its maximum area?

Answer 1

Let ABC be the triangle such that the side BC = a = 4 cm. 

Also, the perimeter of the triangle is 10 cm.

i.e. a + b + c = 10 

∴ 2s = 10 

∴ s = 5 

Also, 4 + b + c = 10 

∴ b + c = 6 

∴ b = 6 – c 

Let ∆ be the area of the triangle.

Differentiating both sides w.r.t. c, we get

∴ by the second derivative test, ∆ is maximum when c = 3. 

When c = 3, b = 6 – c = 6 – 3 = 3 

Hence, the area of the triangle is maximum when the other two sides are 3 cm and 3 cm.