# Problem related to a given diagram

I came across the above problem but do not know how to tackle it. Can someone point me in the right direction? Thanks in advance for your time.

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## 4 Answers

Look at the no. of squares in one triangle. Express the total no. of squares in some form using it.

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How many squares are there on each side of the line?

How many squares are there all together?

Which of the four given equations is related to this?

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I counted that total number of squares on each sides of the line are $11$ and $8$ which means there are total $88$ squares in total.But after that i can not relate it with one of the four given relations... – learner Jan 28 '13 at 16:50
@learner Think of it not in terms of this exact image, but for such triangles in general. Let $n$ be the number of squares across the leg of one of the triangles of squares... – Jonathan Christensen Jan 28 '13 at 16:51

Total number of squares in the upper(lower) triangle = $1+2+3+..n$

The upper and lower triangles make a rectangle.

$2\times($number of squares in the triangle$)=$ total number of squares in the rectangle

$=$ number of square(vertically) $\times$ number of squares horizontally

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It seems to me that the first sum represents one triangle because one triangle is 1 square then 2 squares then 3 squares ... all the way to 8 squares so n(n + 1)/2 plug in 8 gives 8(8 + 1)/2 which is 36. The 3 dots on top seem to represent an orientation reference and the diagonal split is like a mirror plane so as u can see the triangle on the right is what you would expect to see reflected. Im not totally sure that this is correct, although if you look at what the sum is doing, the sum is actually 72 before dividing by 2, so [n(n + 1)] <-- this expression is building up the entire square and the final operation of dividing by 2 gives the correct sum of 1 + 2 + ... n, hence the image...perhaps.

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In mathematics, you cannot really say "seem to". You have contributed nothing new to an already answered question. – Shailesh Jan 4 at 2:54