What am I missing in this math problem?

Asked by LostInParadise (32183

) July 31st, 2018

I was looking through this online material. It gives a motivational algebra problem about a flagpole at the very beginning in the prolog. How was the equation obtained? I tried to set it up and ended up with a messy fourth order equation.

Here is the approach I took. Label as y the distance in the After picture from the end of the building on the ground to the top of the flagpole. From triangle similarity, we get x/10 = 10/y, giving y = 100/x. Then I used the Pythagorean equation for the large triangle: (10+x)^^2 + (10+y)^^2 = (100 – x)^^2. I plugged in the value for y, multiplying everything by x^^2 to clear the denominator to get a fourth order equation that looked nothing like the equation in the book.

I plugged in the values given for x given in the book and the values were pretty close.

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7 Answers

Try solving it as three triangles and Pythagorean theorem. I think that would work.

Tropical_Willie (31435

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You must have miscalculated. After multiplying by x^^2 I get the same result as the author.

flutherother (34864

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Response moderated (Unhelpful)

@flutherother , Could you show your work? With an x^^2 term and a 1/x^^2 term you need to multiply by x^^2 to clear the denominator, and that changes the x^^2 term to a x^^4 term.

LostInParadise (32183

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Would someone please show me where I miscalculated. I get (10+x)^^2 + (10+y)^^2 = (100 – x)^^2, where y = 100/x. Expanding (100 – x)^^2 includes a value of 10000, which is nowhere near what the book has.

LostInParadise (32183

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I caught my error. The x^4 terms cancel. The large numbers are not a problem because the coefficients of the remaining terms are all divisible by 20.

LostInParadise (32183

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