Right Angled Possibilities
If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?
Age
14 to 16
Challenge level
Problem
If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 2 possibilities
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$5^2 + 6^2 = 25+36=61$
$\therefore$ thrid side is $\sqrt{61}$
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$6^2 - 5^2 = 36-25=11$
$\therefore$ thrid side is $\sqrt{11}$
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Impossible since the hypotenuse should be the longest side
$\therefore$ there are only 2 possibilities.