# A strange tube in my homework!?

To calculate the cost of painting his silo, a farmer must find its height. The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below. Approximate the height of the silo. Relevance
• i. They are similar triangles.

ii. The smaller triangle has sides 10 and 5

iii. The side that is 5 feet in the small triangle is equivilent to the side that is 10 feet on the large triangle.

iv. Therefore the scale factor is 2

5. If the other side of the small triangle is 10, it follows that the equivilent side of the large triangle will be 2 x 10 = 20

vi. Add the height of the man

Answer 5 + 20 = 25 feet.

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• because of the right angles [two of them in the diagram], the triangles they are part of have the same shape, size excluded.  from A squared plus B squared equal C squared, we know that the length of the hypotenuse from farmer to ground at silo base is sqrt(ten squared plus five squared) or sqrt (125).  the smallest part of the larger triangle [the one with the square at the farmer's eye] is comparable, except for scale, to the smallest part of the smaller triangle, which he know is five feet.  it follows that the approximate height of the silo is hypotenuse times hypotenuse divided by 5 ... this is sqrt (125) times sqrt (125) divided by 5, or 125 divided by five, or 25 feet.  [the scale factor between the two triangles is sqrt(125)/5.]  QED

Source(s): grampa. I remember that geometry stuff even though it was 53 years ago.
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