Re: B^2+2AD or (A+D)^2-C^2
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13 Sep 2023, 13:00
I believe this question was posted by another user in the forum, so this solution isn't entirely my own. (Not copied and pasted from the other solution post, I just know how to solve the problem from this other post)
First, you simplify the two options given.
(a+d)^2 - c^2 = a^2 + 2ad + d^2 - c^2
Since it's a quant comparison problem, you can subtract stuff from the choices given you do it to choice a and b.
Choice A: b^2 + 2ad
Choice B: a^2 + 2ad + d^2 - c^2
Since both choices have 2ad, you can subtract it. This leaves
Choice A: b^2
Choice B: a^2 + d^2 - c^2
To make things easier by only adding, add c^2 to both choices.
Choice A: b^2 + c^2
Choice B: a^2 + d^2
Then, look at the figure. When an angle is larger, the opposing side also larger. However, if the side between two different angles (like 88 and 92) is the same, you can compensate for different angles by drawing the vertex of the angle closer or farther from the same side. For example, a larger angle's vertex will be closer to the side versus a smaller angle's vertex.
From this concept, you know that sides a and d are longer than sides b and c since the angle between sides a and d is 88 (smaller compared to the angle between b and c which is 92). Since a and d's angles are larger than b and c, a^2 + d^2 will also be larger than b^2 + c^2.
B is the correct choice.