Solve this family (lighthearted) argument

[23Squared]

Son has homework that is causing some lighthearted arguing. (year 9)

The question is thus:

Mary says that there is only one way to draw a square with an area of 23cm squared. Do you agree? Explain.

Son says: No, because the rectangle can be DRAWN in a different orientation. (portrait or landscape) It can be DRAWN starting on the top line or starting from one of the sides.

Mother says: ok but that is not what they are looking for, they are asking for the proof - so one pair of sides should add to an odd number, other pair of sides should add to an even number, 19 + 5, 21 + 2, 17 + 6 etc.

Father says: They should have worded it that way then!

Disclaimer: one or more mother and son members may be on the spectrum

Son says I will get thrashed with this question. He has threatened to sign up and argue his case!

A square is not a rectangle. A square has four equal sides.

Yes agree with PP, the question says a square...

Shit. Wrote the wrong question!

Mary says that there is only one way to draw a rectangle with an area of 23cm squared. Do you agree? Explain.

First, we need to know if it's a question about a square or a rectangle. The two potential scenarios are quite different...

Ok yes the. You are correct. They are looking for the proof, not whether you can physically draw the shape in only one way.

Oops, cross posted

Its a rectangle with area 23 cm squared.

There is only 1 way to draw a square of area 23cm^2 and that is to draw a square of sides just under 5cm long.

If it says rectangle in the question and wants sides to be whole cm then there is still only one was 1x23 as 23 is a prime number and so has no factors other than 1 and 23.

Mum needs to learn what area means.

Dad needs to learn that maths questions wording are often worded like this and he and son need to just go with it otherwise they will have many unhappy years ahead of them.

It could be also drawn so it looks more like a diamond. Even if it was a square. But since it’s a rectangle there can be different lengths than can multiply up to 23cm squared.

If they don't need whole cm then there is a counter example of 0.5cm x 46cm which also gives an area of 23cm^2.

I agree with mother. There is more than one way to draw the rectangle I. E different lengths of the sides

Basically in maths congruent shapes are considered the 'same' even if oriented differently.

Son wants to point out that maths is meant to be black and white. They gave me a question, I gave a correct answer to that particular question. They were looking for an answer to a different question.

Mum says there is no mention of whole or decimal numbers and therefore it could still be as listed in the OP.

Dad has retreated to his phone and beer.

Teen ouch
1x23
2x11.5
Etc

Son is now saying MN is an echo chamber!

He is asking on Reddit!

The pairs of sides (short multiplied by long) need to make the 23 cm squared, so your son could state that yes, there is more than one answer and then give examples.

How old is son?
When he is doing maths he needs to answer in a mathsy way.

Otherwise if old enough, he might enjoy the Professor Layton games on the Nintendo DS, which sometimes have irritating tricks to them, but are often nice logic puzzles.

(Would it help if you told your son I have a maths degree and a teen who has done maths GCSE and another about to start KS4? If he says there is more than one way because he can use a different colour pen or whatever, he'll get zero marks.)

Son is 14!!

He says he 'answered the question that is asked'

He is preapproving my posts. otherwise I would say the answer is yes, but his proof is wrong

Teen - yes, the orientation isn't the issue - it the WAY you DRAW it! ie. down, across, up, across or down, down, across, across.

Teen - he says he didn't mention pen colours, it is the WAY YOU DRAW it aspie

I said that the examiners won't care if he is technically correct. They want the proof. And we are back to the wording of the question issue

I'm gonna hate GCSE prep arent i and his teacher might possibly have a breakdown

But you can draw it differently with different pens...

At 14, so presumably y10 like my DD2, he needs to get with the programme.
My DD1 has dyspraxia which has some Autism cross over. She really struggled with GCSEs initially because she answered the question in front of her, and not what they wanted. So 6 mark questions in science would have 1 sentence answers etc.
She had to work really hard to understand that even if they didn't say 'and give detailed explanations' then that was still what they wanted. We then had to work with her to help her understand what extra info they were looking for.

But for this question, it is a MATHS question not an ART one. The answer is not about how the lines are drawn but what the resultant shape is.

Oh let him do it his (wrong) way and he can have the discussion with his maths teacher.