Please help with MATHS homework - calculating area with Unknowns.

[NotQuintAtAllOhNo]

Rectangles A and B have the same area.

A:
3cm
(3x+1)cm

B:
5cm
2x cm

1. What is the area of rectangles A and B
   
2. What is the perimeter of rectangle B?
   
3. If rectangle A was enlarged by a scale factor of 3, what would the enlarged area be.
   
4. If rectangle A was enlarged by a scale factor of 1.5, what would the enlarged area be.
   

I am as stumped as he is.

[FivesAndNorks]

Area of A is 3(3x+1) (assuming figures are the two sides' lengths)
B is 10x (5 times 2x)

perimeter is adding all sides together

so A: 3+3+(3x+1)+(3x+1) = 6x+8
B: 5+5+2x+2x = 10+4x

Does that make sense

[NotQuintAtAllOhNo]

It makes sense.

Should we not find what the X is?

[FivesAndNorks]

And we know they have the same area, so 3(3x+1)=10x

which means 9x+3 = 10x
so x=3

so the area of each is 30

not totally sure what they mean by scale factor - am guessing they mean each side is extended by that factor, rather than just the overall area - either way, should be calculable

[NotQuintAtAllOhNo]

I am with you up to this point: 3(3x+1)=10x

But I dont see how this is worked out :

which means 9x+3 = 10x
so x=3

(more than 20 years since I saw maths like this)

[NotQuintAtAllOhNo]

Oh I see

9x+3 = 10x

10x - 9 x = 3
x=3

(dim)

[NotQuintAtAllOhNo]

How do we enlarge A by a scale factor of 3? Just multiply?

[noblegiraffe]

Multiply the length of each side by 3 then calculate the new area. Hopefully you'll find the new area is 9 times the original area.

This seems a bit difficult for primary? What level is DS?

[NotQuintAtAllOhNo]

level 5 year 6

[noblegiraffe]

That homework is pushing level 7! No wonder he's finding it hard :)

[NotQuintAtAllOhNo]

Thanks both of you, we worked it out.

Luckily he grasps it easily once explained.
Level 7? No wonder....

[noblegiraffe]

I would set something like that for Y9 or maybe top set Y8, and expect some of them not to get it.
I suspect that the teacher has misjudged things slightly if that has been set for everyone. Please write a note to say extensive help was needed otherwise the teacher might continue to press ahead thinking 'well Little Johnny got it'.

[NotQuintAtAllOhNo]

They don't all get the same homework luckily, he told me yesterday that he is just below the 4 children in his class which are working towards the level 6 exam, there are 4 different groups in his class. (I dread to think what homework these children get)