A right angle triangle has sides whose lengths are $2$-digit integers. The digits of the length of the hypotenuse are the reverse of the digits of the length of one of the other sides. Determine the smallest possible length of the hypotenuse.

Smallest possible length of the hypotenuse = 65

Step-by-step explanation:

Given - A right angle triangle has sides whose lengths are $2$-digit integers. The digits of the length of the hypotenuse are the reverse of the digits of the length of one of the other sides.

To find - Determine the smallest possible length of the hypotenuse.

Proof -

The possible Pythagoras triplets of a right angled triangle with 2 digit integers are -

(11, 60, 61)

(12, 35, 34)

(13, 84, 85)

(16, 63, 65)

(20, 21, 29)

(28, 45, 53)

(33, 56, 65)

( 36, 77, 85)

(39, 80, 89)

(48, 55, 73)

(65, 72, 97)

But, Here Given that

The digits of the length of the hypotenuse are the reverse of the digits of the length of one of the other sides.

So, There is only one possibility that satisfy the condition.

and that is, (33, 56, 65)

So, we get

Length of one side = 33

Length of second side = 56

Length of hypotenuse = 65

So,

Smallest possible length of the hypotenuse = 65

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50