In a standard test, the children who score exactly and above the 97th percentile will be considered for a scholarship. The scores of the standard test are normally distributed, the mean of the distribution is 56, and standard deviation is 22. Which score corresponds to the 97th percentile? Round your answer to two decimal places.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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