- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,932

Find the perimeter of this triangle.

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,932

Find the perimeter of this triangle.

- Mar 31, 2013

- 1,349

Find the perimeter of this triangle.

possible onlly if a = 3 sqrt(2) and b = 2 sqrt(3)

so c(diagonal) = sqrt(30)

so perimeter = 3 sqrt(2) + 2 sqrt(3) + sqrt(30)

- - - Updated - - -

- Thread starter
- Admin
- #3

- Feb 14, 2012

- 3,932

Hi=> sqrt((a - 3 sqrt(2))^2 + 1) + sqrt((b - 2 sqrt(3))^2 + 4) < = 3

possible onlly if a = 3 sqrt(2) and b = 2 sqrt(3)

Thanks for participating and I think it's necessary to

Or perhaps it's very obvious and it's just me don't see how it is so?

- Mar 31, 2013

- 1,349

I think I owe an explanationHikaliprasad,

Thanks for participating and I think it's necessary tostatewhy the given inequality is true iff $a = 3 \sqrt{2}$ and $b = 2 \sqrt{3}$, what do you think?

Or perhaps it's very obvious and it's just me don't see how it is so?

now we are having

sqrt(1 + x) + sqrt(4 + y) <= 3 with x,y > 0

if x = 0 and y =0 then LHS = 3

if x > 0 then y = 0 then LHS = 2 + sqrt(1+x) > 2 + 1 > 3

similarly for y > 0 and for x and y > 0 LHS > 3

x = (a - 3 sqrt(2))^2

y = (b - 2 sqrt(3))^2

or