Question 1189324
<br>
As the other tutor points out, the question as posed, with four answer choices, is easily solved because only one of the choices is possible.  For the problem to be written in a way that makes the student do some actual problem solving, there would have to be a 5th answer choice "e. none of the above".<br>
So let's go ahead and show that answer choice b actually gives a triangle with perimeter 15.<br>
With the line having a slope of -12/5, the x- and y-intercepts are of the form (5a,0) and (0,12a).  So the lengths of the two legs of the right triangle are 5a and 12a; that makes the length of the hypotenuse 13a.<br>
The perimeter is then 5a+12a+13a=30a; since the perimeter is 15, a=1/2, and the x- and y-intercepts are (5/2,0) and (0,6).<br>
Now we have a line with slope -12/5 and y-intercept 6:<br>
y=(-12/5)x+6
(12/5)x+y=6
12x+5y=30<br>
Yes, answer choice b is indeed correct.<br>