Ok so I have the following question:
Each angle in ∆QRS has a degree measurement of either x or y and the angles are expressed by the equation 2x + y = 180
Quantity A
The perimeter of $\triangle QRS$
Quantity B
17
Which of the following statements are true?
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
My initial try was that as the angles are 2x+y=180 the triangle is isosceles and RS must be $7$, thus the perimeter of $\triangle QRS$ is $7+7+4 = 18 > 17$ and the correct answer is A.
Apparently, the correct answer is D, as someone noted that QS can also be $4$, so $7+4+4=15 < 17$, so it can't be determined. Can anyone explain why is that? Is it because QS is not fixed, so it could also take $4$ as value?
Also isn't the graph misleading in order to make you think only of the first choice? Thank you!
Your reasonement is correct. In fact, without further informations we can't determine the angle adiacent to the base. So there are two different possibilities for the perimetre: $$P=7+7+4=18>17$$ Or: $$4+4+7=15<17$$ So the correct answer is $D$ because we don't have much more informations.