Can anyone help with some maths homework please?

[troppibambini6]

Hi my dd has an online maths tutor group tomorrow and has a sheet to do.I wanted to go through it with her before the lesson but I'm finding it tricky area and perimeter was never my strong point

The perimeter of a rectangle is 36m which of the following could be the area of the rectangle.

A. 24m squared
B. 36m squared
C. 28m squared
D. 72m squared
E. 81m squared

If you could tell me in a way a 10 year old could understand (and a 43 year old) I would be really grateful. I'm sure it's something really simple but I just can't see it!

perimeter = 2(a + b) where a,b are side lengths.
So as perimeter is 36, a+b=18
so then go down with the different possibilities for 2 whole numbers adding up to 18

So a=9, b = 9, area= 81 (you can argue that in this case it's a square so doesn't count, but a square is just a special (maths term "regular") rectangle, so I would count it.)
a=8,b = 10, area = 80
a=7,b=11, area = 77
a= 6, b = 12, area = 72
a=5, b=13, area = 65
a=4, b=14,area = 56
a= 3, b =15, area = 45
a=2, b = 16, area = 32
a= 1, b = 17, area = 17

If x is the length and y the width:

2x + 2y = 36. (Perimeter)
xy = area

Easiest way would probably be to figure out all the combinations x and y could be (number bonds to 18, excluding 0+18) then work out the area of each pair.

There's probably a less tedious way to do it using algebra but I'm not sure if a 10 year old would have encountered algebra yet.

2a+2b =36
ab = 24 or 36...

Then substitute for a or b?

It’s D and B.
I worked it out by dividing 36 by 4 (9)which would tell you the length of the sides if it was a square. As it’s a rectangle, you need two longer sides and two shorter sides. So instead of 9x9 to work out the area, you would have as options:
10x8=80
11x7=77
12x6=72 Tick!
13x5=65
14x4=56
15x3=45
16x2=36 Tick!
17x1=17

Hope that helps!

Start by looking at the possible ways to find those rectangle areas:

A. 24cm squared could be 12 x 2 or 6 x 4.

If 12 x 2 then the rectangle would have two sides of 12cm + two sides of 2cm. Add them together and it would be a perimeter of 28cm - so no good.

If 6 x 4 then it would have two sides of 6cm and two of 4 cm. Add them together and you would get 20cm - so no good.

Do the same with each of the rectangle areas until you find one that adds up to 36cm.

Thank you so much! Me and older dd did just figure it out but wondered if there was an easier way of working out A and B or if it was just a case of using number bonds.
Also apologies
E- was 81cms squared not metres
So obviously there as one to trip them up!!

For an equalateral triangle the answer is 72
The perimeter is measuring all of the outside.
The perimeter of the triangle given is 36m. Triangle has 3 sides so divide 36 by 3 to find size of each side
36 ÷ 3 = 12
To then find the area multiply 1 length by 1 width
12 x 12 =144 like you would with rectangle but because its a triangle you then half this number
144 ÷ 2 = 72.
Hope this helps x

I did it as x + y = 18 (2 of the sides add up to half of the perimeter of 36)
Go through the options of lengths that add up to 18 e.g.

1 x 17 (17 area)
2 x 16 (32)
3 x 15 (45)
4 x 14 (56)
5 x 13 (65)
6 x 12 (72) - answer D
7 x 11 (77)
8 x 10 (80)
9 x 9 (81) - also works but is a square rather than a rectangle

A rectangle has 4 sides, made up of 2 equal pairs. Top and bottom are the same length, left and right are the same length.

The perimeter is calculated by adding the length of all 4 sides.
The area is calculated by multiplying one side of each pair, so either (top x left) or (bottom x right) etc

If we know the perimeter is 36 then we know that all 4 sides add to a total of 36.

So we know top(x2) + left(x2) =36
Look at the different ways to make up 36.

Go through each of the possible areas and find the multiples that fit.

In this case option D, the area is 72 makes sense.
72 can be made up of 6x12.
So if we fit these numbers into the calculation for the perimeter you have,

(6x2) + (12x2) = 12 + 24 = 36

I really hope this makes sense. X

@ChilliWillies

It’s D and B. I worked it out by dividing 36 by 4 (9)which would tell you the length of the sides if it was a square. As it’s a rectangle, you need two longer sides and two shorter sides. So instead of 9x9 to work out the area, you would have as options: 10x8=80 11x7=77 12x6=72 Tick! 13x5=65 14x4=56 15x3=45 16x2=36 Tick! 17x1=17

Hope that helps!

16 x 2 is not 36!

Sorry I just realised it was a rectangle not a triangle 🤦‍♀️