 ## Question

primary 6 | Maths | Measurement

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##### DS

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Please assist. The 3 rhombuses are of different sizes but can I divided equally? It doesn't make sense....

Date Posted: 4 months ago
Views: 22
J
4 months ago
There are 3 rhombuses, let's call them small medium and large.

Perimeter of all 3 rhombuses

= Perimeter of small rhombus + perimeter of medium rhombus + perimeter of large rhombus

= 4 lengths of small rhombus + 4 lengths of medium rhombus + 4 lengths of large rhombus

Since total perimeter of all 3 rhombuses
= 60cm,

4 lengths of small rhombus + 4 lengths of medium rhombus + 4 lengths of large rhombus = 60cm

1 length of small rhombus + 1 length of medium rhombus + 1 length of large rhombus

= 60cm ÷ 4 = 15cm

We have 3 equilateral triangles, small medium and large.

From the figure we can see that :

Length of 1 side of big triangle = length of 1 side of big rhombus

Length of 1 side of medium triangle = length of 1 side of medium rhombus

Length of 1 side of small triangle = length of 1 side of small rhombus

Perimeter of figure

= 3 sides of each rhombus + 2 sides of each equilateral triangle

= 3 sides of each rhombus + 2 sides of each rhombus

(Because we already established that the sides of the triangles are equal to their corresponding rhombuses)

= 5 sides of each rhombus

= 5 sets of lengths (1 big ,1 medium,1 small rombus length for each set)

= 5 x 15cm

= 75cm

The rhombuses are of different lengths based on their appearance. Though it is possible that they are equal and merely just not drawn to scale, this will have to be mentioned by the question. However there is no mention of this.

We cannot establish their individual lengths as no info is given. And we also have no sure way to determine if they are equal or not.

But we know that we can group their lengths into 4 sets, each set having 1 small, 1 medium and 1 big rhombus length. And 4 sets equals 60cm.

Then 1 set is 15cm.

So we don't need to figure if they are the equal or not, or what each individual length is to solve this question.

Most importantly, never assume they are equal. For this question, assuming so will get you to the same answer of 75cm (you can try) but it's conceptually incorrect.

In other questions, assuming so is most likely to lead to a wrong answer.
DS
4 months ago
Thank you for your information. I appreciated it.
J
4 months ago
Welcome.

Note that the answer is 75cm instead of the 90cm the other person posted as we can only count 3 sides of each rhombus instead of the 4. The inner side is already blocked when you consider the whole figure.

clear {{ downvoteCount * -1 }} Downvotes
1st
You can divide equally when you group the 3 different sides of the rhombuses into a set.

I hope it helps.
Date Posted: 4 months ago
J
4 months ago
The question asks for the perimeter of the figure. You included all 4 sides of each rhombus in your working.

The inner side is sandwiched by the triangle so it's no longer part of the outline of the figure and thus it cannot be included in the perimeter.

You should only be counting 3 sides of each rhombus. 