Geometry Foundation Quiz #2 query

hello! i have a few doubts.

here is question 1:

i remember Greg mentioning that if the perimeter is held constant, the area of the regular shape will be more than the area of the irregular shape, and used square and rectangle as an example. then why is A wrong?

question 2:


with no other information given, how can it be assumed that the two quantities are equal?

last question:


aren’t the two triangles congruent? and doesn’t that imply that the area is going to be the same? why is the answer here D?

Rectangles can be squares.

See Angles in the Same Segment Are Equal - Steps, Examples & Worksheet

Why do you think the two triangles are congruent?

thank you for the link! i’ll check it out

  1. haven’t they explicitly mentioned rectangle? sure squares are also rectangles. could you provide an example where quantity A isn’t bigger?

  2. nevermind, scratch that. i forgot the SAS congruence works when the angle is formed by the two equal sides. thank you!

When the rectangle is a square.

I wanted to follow up on this as I understand from your explanation since square is also a special type of rectangle we would mark option D but then where would the applicability of the theoram - Given the same perimeter, if area needs to be maximized it needs to be regular be valid. So, my question is how could this be asked in the similar format of this question like could you share any example where the same question can be asked that adheres to the property mentioned above. I just want to understand how can I differentiate between the 2 questions.
@Leaderboard please… :pray:

Which two?

one where we are asked to apply the principle “Given the same perimeter, if area needs to be maximized it needs to be regular” and one where we need to differentiate that with the given parameter rectangle could also be square so area can’t be determined. I am unable to understand how the theorem question can be asked where we would choose that square has a larger area than rectangle with the same parameter.

You’re not asked for the area in the first case - the second case is probably saying that you don’t know what the area is. Without knowing the exact question, can’t comment further.

Okay, thanks for clarifying.