Where do i start with this? it is a calc question. i thought perhaps relating the height to the length to get everything in terms of one variable by setting both legs to equal the hypotenuse with the pythagorean theorem but i'm having trouble. dunno if that's even a good way of going about it.

See below.

Step-by-step explanation:

You are correct in your approach. You can calculate the hypotenuse via Pythagoras, so you will know |AB|.

Then, I would do the following:

Denote the upper left corner of the rectangle that intersects with AB, a point D. Then call "a" the distance |AD|. Call the rectangle height x, and width y.

Use triangle similarity to set up a system of equations: A choice of "a" induces a rectangle x-by-y where

Now, we can get 2*(x+y)  (aka, the perimeter) from those two equations:

which is a function of one variable "a" and you can  minimize that using a derivative.

But here's where I am finding this problem not a very good one: as you surely noticed the perimeter is linear in "a." As such, it's derivative will be constant and uninteresting. Even without the derivative you can see that to minimize the perimeter expression above, you should minimize "a."  In other words "a" should become infinitesimal and the rectangle will be basically (epsilon) by (|AC|-epsilon), where epsilon is as small as possible.

I imagine this problem would become only then "interesting" (in that a derivative would give you something), if the question was to minimize the area of the rectangle.

Please feel free to let me know if you have questions.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

the answer is 13 cm