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More ways to get Braingle...

Cornered

Math brain teasers require computations to solve.

 

Puzzle ID:#30834
Fun:*** (2.64)
Difficulty:*** (2.67)
Category:Math
Submitted By:norcekrius****
Corrected By:calmsavior

 

 

 



When Nora and Corman stopped by the school to whisk Monette off to lunch, the poor principal was hemmed in by two tall, annoyed math students.

"My answer is right, and I want my three points!" the blond one cried.
"But it's not the answer Mr. Collins left on the key!"
"He's wrong," the other one insisted. "My answer is right!"
Corman leaned over to whisper in Nora's ear, "Does she need our help?"
"Yours, probably. Mr. Collins is at a conference for the weekend, and Monette took his math class. It looks like she handed back an exam."
"I teach math. Can I help?"
All three talked at once; Monette was as frustrated as the two students. While they jabbered, Corman managed to read the problem in question:

"My house is built on a strangely-shaped lot, so my back yard is a right triangle with an area of 840 square feet. Each of the three sides measures an integral number of feet. If I want to stake my dog so that he can reach the entire yard, how long must his rope be?"

Monette finally pulled rank on the adolescents. "It's not really your problem, but I'd be glad of some help. Mr. Collins marked their papers wrong; their answers don't match his. The students *sound* right, but math was too long ago for me; I'm not sure. To make matters worse, they don't even agree with each other."
"I see," said Corman, playing for time while he mentally checked the answer on the key in Monette's trembling hand. "That's the answer Mr. Collins left you?"
"Yes," she began.
"The right answer is 8 feet shorter," the blond claimed.
"No, it's a lot longer," insisted the other.
Corman held up a hand for peace. "Actually, you *could* all be correct."
"How can there be ... oh, it's one of those problems with an infinite number of right answers, because we're missing a clue?"
"Well, let me see your work." The students handed him their papers; he followed the algebra, nodding for almost a minute.
"Nice work. You've found the only three right answers."
"How can there be exactly three? Usually, it's one, two, or infinity?"
"Usually, you're right. Welcome to discrete math. When you restrict things to whole numbers sometimes they don't work out so simply."

How much rope did Mr. Collins really need?

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