If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I.	28
II.	36
III.	42 Choices.
A) I only	B) II only	C) I and II only	D) I and III only	E) I, II, and III
x+y=30 &amp; y+z=20 so x+2y+z=50   x+y+z=50-y   If perimeter is 28 then y=50-28= 
<gadget id="calculator">50-28</gadget>
<output>22</output>
22, and y+z=20 z cannot be negative. I is out.   If perimeter is 36 then y=50-36= 
<gadget id="calculator">50-36</gadget>
<output>14</output>
14. z=6, x=16. no problem here.   If perimeter is 42 then y=50-42= 
<gadget id="calculator">50-42</gadget>
<output>8</output>
8. x=22, z=12. x cannot be greater than sum of y &amp; z. III is out.   II only is answer.
<result>B</result>
If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I.	28
II.	36
III.	42