Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?

Largest perimeter of the triangle =  

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, we get,

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

At x = ,

Then, by double derivative test, the maxima occurs at x =

Thus, maxima occurs at x = for P(x).

Thus, largest perimeter of the triangle =  

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl