Carcass wrote:
The sides of a triangle are 1, x, and \(x^2\). What are possible values of x? Indicate all possible values.
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
F. 3
G. 3.5
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then:
|A-B| < third side < A+BNow let's see what measurements we get for each value of x.
A. x = 0.5. So 1, x, and x² become 1, 0.5 and 0.25. Here, it is NOT the case that
|0.5 - 0.25| < 1 < 0.5 + 0.25 ELIMINATE A.
B. x = 1. So 1, x, and x² become 1, 1 and 1. Here, it IS the case that
|1 - 1| < 1 < 1 + 1 B WORKS
C. x = 1.5. So 1, x, and x² become 1, 1.5 and 2.25. Here, it IS the case that
|1.5 - 1| < 2.25 < 1 + 1.5 C WORKS
D. x = 2. So 1, x, and x² become 1, 2 and 4. Here, it is NOT the case that
|1 - 2| < 4 < 1 + 2 ELIMINATE D.
E. x = 2.5. So 1, x, and x² become 1, 2.5 and 6.25
Here, it is NOT the case that
|1 - 2.5| < 6.25 < 1 + 2.5 ELIMINATE E.
F. x = 3. So 1, x, and x² become 1, 3 and 9. Here, it is NOT the case that
|1 - 3| < 9 < 1 + 3 ELIMINATE F.
G. x = 3.5. So 1, x, and x² become 1, 3.5 and 12.25. Here, it is NOT the case that
|1 - 3.5| < 12.25 < 1 + 3.5 ELIMINATE G.
Answer: B, C
Cheers,
Brent