Carcass wrote:
Attachment:
GRE triangle (6).jpg
Quantity A |
Quantity B |
\(a^2+c^2 \) |
\( b^2\) |
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
It is not fully necessary to go for x's value to solve this exercise, however, I will post the full solution:
we know that in any triangle, its inner sides must sum 180°, therefore,
\((2x - 30) + (2x-50) + (x+60) = 180\)
\(x = 32\)
replacing x (I named every angle with greek letters),
alpha = 32+60 = 92.
beta = 2*32 - 30 = 34.
gamma = 2*32 - 50 = 14.
Here comes the conceptual part:
crucial concepts:1) there is a direct relationship between the side length and the opposite angle to that side.
(the larger the angle, the larger the side)2) the pythagorean theorem says that in every
right triangle, the following rule must hold: \(a^2 + b^2 = c^2\) (I am not using equivalent letters)
First of all, we already know that it is
NOT a right triangle. Then, why is this theorem useful?. Because it gives us a cut off point: when the angle is 90°, the square of the opposite side is equal to the sum of the square of each of the remaining sides. But, having said that, what happens if the angle is greater than 90°?. Due to the rule (1), it is straightforward that \(a^2 + b^2 < c^2\), because we know that in terms of proportions the side C becomes relatively bigger (alpha=92).
Therefore, and using the problem's notation: \(a^2+c^2 < b^2\). B>A. Option B