More maths problem help please!

[annie987]

Hi
Please can anyone give a bit of help with these maths problems.
According to the maths teacher, there should be no need to use any decimal measurements nor simultaneous equations.
Thanks

@Nooz but, in problem one, if the length of one side of the eastern-most square is 5cm, surely the other side is a decimal (i.e. 3.2 cm) in order to make its area 16cm squared? I mean it looks the same length as the 5cm on other side but maybe you’re supposed to disregard that? That’s what threw me.

It's impossible to do the diagram as it is without decimals.
Step 1: area of middle rectangle is 24 (already agreed)
Step 2: find width of middle rectangle is
24 / 5 = 4.8
Step 3: vertical area = 21 + 24 + 27 = 73
Step 4: total height (?) = 72 / 4.8 = 15
See attached for clarification.

Oops! 73 should be 72

If we rerun it with a height of 4, the area of the total horizontal part is 48, leaving 12 for the centre.

Left box 4 high x 5 WIDE
Right box 4 high x 4 wide

Total width is 12 less the widths above leaves a width of 3 for the centre box.

Yup must be because...

Centre box 4 high x 3 wide gives the 12 area our first step found

Now we know the boxes top to bottom are 21, 12, 27

Our last step told us their common width is 3 because the width of the centre box is 3.

Top box 7 high x 3 wide
Centre box 4 high x 3 wide
Bottom box 9 high x 3 wide

Total height 20

I PROMISE the teacher had made an error in labelling the diagram.

This is such a simple human error and really really frustrating!!! Took me a while to spot it. It's the sort of thing that can slip by even when double checking.

You're owed an apology andfor keeping at it. Fair play and respect!! Xx

^Step 2: find width of middle rectangle is
24 / 5 = 4.8^

It's not compulsory to reduce 24/5 to 4.8 though. It's actually easier if you don't. Just leave the width as a fraction 24/5, then:-

72 / (24/5) = 72 5 / 24 = 3 24 5 / 24 = 3 5 = 15

Seriously it's a typo and the height labelled 5 should be 4!!

The op has been told this is an integer based problem

Someone just muddled around the dimensions of the left hand box when they labelled the diagram! X

I think @Nooz must be right - a typo is the only explanation that doesn't lead to a much more tricky problem. I do think that the 5cm labelled on the left must be 4cm instead.

For all three, they're almost closer to being logic problems than maths problems.

Just reading the answers has me confused!

There's nothing wrong with qu.1

@RandomLondoner has it

answer for the first one is: 7
the second one: 35
third one, i am not sure if there is a problem with the question so not bothering much.

5cm * 12cm = 60cm^ (horizontal rect.)
60cm - 20cm - 16cm = 24cm (centre rect.)
21cm + 24cm + 27cm = 72cm (verticle rect.)
20cm^ / 5cm = 4cm (left rect.)
16cm^ / 5cm = 3 1/5cm (right rect.)
12cm - 4cm - 3 1/5cm = 4 4/5cm (centre rect.)
72cm^ / 4 4/5cm = 15cm (answer)

Not seeing any errors in the question.

i think the answer for the third one is : 1.

Third question, as Bluebell says, the height they're looking for is 9.

Lengthier explanation:

Label the areas inside 17cm2 is A, 18cm2 is B, 19cm^2 is C. First unknown is d and second unknown is e. The unknown height is h

Then look at each measurement of width given and work out what areas they cover.

1st width of 7cm:
7xh = A + e + B

2nd width of 8cm:
8xh = B +f + C

3rd width of 9cm:
9xh = e + B + f

so if we add the first and second widths:
7xh + 8xh = A + e + B + B + f + C
which gives us:
15xh = A + 2B + C + e + f

then take away the third one:
15xh - 9xh = A + 2B + C + e + f - ( e + B + f)
which gives us:
6xh = A + B + C
so 6xh = 17 + 18 + 19
6xh = 54

h = 9

Q1: 15 cm
Q2: 40 cm^
Q3: 9 cm

Hi I agree with 15 for no.1 if decimals were allowed in the calculations but as they are not has to be a typo x

Number 2 is the same - you don't need to use decimals if you leave the fractions and work through like that so it wouldn't violate the no decimals as the answers are integers

So for q1

Total horizontal rectangle is 5x12=60^2
Middle bit is then 60-16-20=24^2
Width of middle is 24/5
Total vertical rectangle is then 21+24+27=72
It's height is then 72 ÷ 24/5 which you solve by multiplying by the reciprocal so it becomes (72×5)/24 which is 15

Agree with @Nooz

If no decimals allowed or required, there MUST be a typo in question 1.

You don't need to use decimals as you can solve without simplifying the fraction. It seems very unlikely that 2 of the questions have errors and more likely that this was their intention

No error in the puzzle. The height is 15 and whilst it's necessary to write down the odd fraction, they are only used as an interim measure and not really involved in any complex calcs.