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| Math Central | Quandaries & Queries |
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Question from alvin, a student: A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If a 15 gallon of water are poured into the trough and if the trough is held level so that a right section of water is an isosceles right triangle, how deep is the water? (231cu.in=1 gal.)
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Alvin,
The volume of water in the trough is the area of the right section of water times the length of the trough. Convert the length to inches, convert the 15 gallons to cubic inches and divide it by the length of the trough in inches to find the area of the right section of water in square inches.
$PQS$ is a right triangle so use Pythagoras theorem to find $|QS|$ in terms of $a.$ Half of this quantity is $|QR|$ and triangle $QRP$ is a right triangle so use Pythagoras theorem again to find $h$ in terms of $a.$ Now you can solve for $a.$
Write back if you need more help,
Penny
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