srini1988 wrote: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
A)I only
B)II only
C)I and II only
D)I and III only
E)I,II and III
First of all, the perimeter CANNOT equal 28
We know this because we're told that x + y = 30, which means the sum of two sides is 30
In order for the perimeter (x+y+z) to equal 28, side z would have to have length -2, which makes no sense.
ELIMINATE A, C, D, and E
Answer: B
On test day, I wouldn't spend any more time on this question.
However, let's keep going. . .
Next, we can show that the perimeter CANNOT equal 42
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
We're told that y + z = 20, which means the sum of sides y and z is 20
The above rule tells us that the third side (side x) must be LESS THAN 20
If x is less than 20, and y+z = 20, it's impossible for the perimeter (x+y+z) to equal 42
Finally, the perimeter (x+y+z) CAN equal 36
If x = 16 y = 14, and z = 6, then all of the conditions are met, AND the perimeter is 36
