Please help with this maths question

[missyB1]

It’s for me not my child

I need to reduce a rectangle by a scale factor of 0.8. The sides currently measure 105mm by 148mm. I’m tying myself up in knots! Is there a formula for this? I’ve tried googling but I’m embarrassed to say I don’t understand the explanations - most of which are for increasing by scale not reducing.
My instinct is to multiply each side by 0.8 but I’m at all sure about that!

Yes times by 0.8

Oh thank you I think I just panicked! It’s a confidence thing with me and maths!

105 x 0.8 = 84
105 - 84 = 21
21mm is the length of the side reduced by scale of 0.8

I think it depends on what you want to reduce by 0.8.
To reduce the area by 0.8, then multiply 105 by 148, and then multiply the result by 0.8 - Original area = 105 x 148 = 15,540, x 0.8 = 12,432mm2
To reduce the sides by 0.8, simply multiply each side by 0.8 - Original side 105 x 0.8 = 84mm. Original side 148 x 0.8 = 118.4mm

Thanks the question said to reduce each side by scale of 0.8 then find the area.

Typical tricky worded functional skills question! If I fail the exam (next week) it will probably be because of the horrible way they word the questions!

@ThreeFish is correct.

You need to reduce it by 0.8.

If you multiply it by 0.8 you then need to take that away from the original length. You can get round this by multiplying the original length by 0.2 instead.

Then when you have the 2 new values for the sides, multiply those together to get the area.

I'm not so sure about that interpretation. If the scale factor is 0.8 then the new length is found by multiplying the original length by 0.8. (No subtraction then required). But a question saying "reduce by a scale factor" would be better worded as reducing with a scale factor, or using a scale factor.

So you have a photo with the exact wording?

Here is the actual question. The scribble underneath is my working out!

Aha! So the wording is clear: "applying a scale factor of 0.8". In which case, the method you have used is correct. I haven't checked your arithmetic, but you are getting the same numbers as Jolonglegs so it looks good to me [ex-Maths teacher].

Bonus for putting the correct units on your answer. Supplementary question: can you convert from square mm to square cm?

Hmmm... divide by 10?? God I’m rubbish at maths which why I’m doing this at age 50, because I failed it at school all those years ago!

That's why I asked the question as it's easy to be caught out: 10mm is 1cm, so you would divide by 10 to convert from mm to cm, but 1 square cm is 10mm by 10mm which is 100 square mm, so divide by 100 for area conversion.

That's why although there are 100cm in 1m, a cubic metre is 100 x 100 x 100 = 1,000,000 cubic centimetres.