JEE Class main Answered

Figure shows the triangle formed by vertices A(2,1) , B(0,0) and ( t, 4)

side AB = √5 unit

side BC =   unit

side CA =   unit

Perimeter P =   unit

To find the maximum or minimum perimeter with respect to coordinate t ,

we differentiate above expression of perimeter with respect to t , equate to zero and try to get the values of t

Above expression is simplified as

By squaring both sides , we get

Above expression is simplified as the following quadratic expression

7 t² - 64 t + 64 = 0

Above quadratic expression has the following roots

t = 8  and t = 8/7

Value t = (8/7) will give minimum perimeter , hence β = (8/7)

Value t = 8 will give maximum perimeter but t is limited to 4 . Hence α = 4