For A)
There are two values: W (width) and L (length)
In the 1st tower there are 4W and 3L.. and they equal 33 (4W + 3L = 33)
In the 2nd tower, there are 2W and only 1L. they equal 13 (2W + L =13)
So If we double the second tower then we will have 4W but only 2L. it will equal 26 (4W + 2L = 26)
Therefore if we take away double the second tower away from the first tower, we will have one length and it will measure 7cm. (4W - 4W + 3L – 2L = L) (33- 26 =7) (L=7)
Now that we know what one length is, we can replace the L on tower 2 with 7 (2W + 7 = 13)
If we take away the 7 we will have 2W + 6. Then you divede the 6 by two and you have your width (3cm)
To work out the perimeter, you will need to add 2W and 2L
This is actually 2 X 3 + 2 X 7. This will equal 20cm
For B)
There are two values: W (width) and L (length)
There are 3W in L because they are on their side and make up 1 length
So we know that L = 3W, that means we no longer need to use L .
Because of this, we know that on the top edge, there are 5W
Whilst on the other side, there are 3W.
Therefore we know that 3W times by 5W equals 60cm2
That means that 15W2 equals 60cm2 (and 15W equals 60cm)
So we need to divide 60 by 15 to get W
Meaning that W equals 2cm
So the width equals 2cm
And the length equals 6 (3 X 2)
So 2 X 2 + 2 X 6 = 16cm
For C)
There are two values: W (width) and L (length)
There are 4W in L because they are on their side and make up 1 length
So we know that L = 3W, that means we no longer need to use L .
Because of this, we know that on the top edge, there are 6W
Whilst on the other side, there are 4W.
Therefore we know that 4W times by 6W equals 600mm2
That means that 24W2 equals 600mm2 (and 24W equals 600mm)
So we need to divide 600 by 24 to get W
Meaning that W equals 25mm
So the width equals 25mm
And the length equals 100 (25 X 4)
So 2 X 100 + 2 X 25 = 250mm
For d)
There are once again, two values: L and W
We know that 5W is 4L because 5 rectangles lying on their side is 4 standing up.
So, if 5W = 4L then L will equal 5W divided by 4.
We know that because of this, 5W X (W + 5W/4) =180
If we times out of the brackets, then we get 5W2 + 25W2/4 = 180
If we divide this by 5, then we will get W2 + 25W2/20 = 36
Since 25W2/20 equals 1.25W2 we can now use that
This means that we can now change W2 + 1.25W2 = 36 into 2.25W2 = 36
This means that now, we can divide 36 by 2.25. It gets us W2 = 16
So we now have to square route 16, it gives us 4.
W= 4
And if 5W/4 is 1.25, then L =1.25W
That means that L = 5 and W=4
So 2 X 5 + 2 X 4 = 18cm
For the last question
You know that along the bottom it will equal B
This means that since there are no parts sticking out (along the side) the top will equal B
Therefore so far we have 2B
We know that along the right side it is A.
We can now count the other side (apart from the bit sticking out) as A
We know this because it is the same length as A.
This means we have 2A
We now have a bit sticking out of the side.
It is called C.
The sticking out bit is on two sides. Both sides equal C.
So both together will equal 2C.
Altogether, we have 2B+2A+2C