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?
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.
Answer: 2 possibilities
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![Right Angled Possibilities Right Angled Possibilities](/sites/default/files/styles/large/public/thumbnails/content-id-5025-right%252520angled%252520possibilities%2525201.png?itok=Ld-zU9j6)
$5^2 + 6^2 = 25+36=61$
$\therefore$ thrid side is $\sqrt{61}$
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![Right Angled Possibilities Right Angled Possibilities](/sites/default/files/styles/large/public/thumbnails/content-id-5025-right%252520angled%252520possibilities%2525202.png?itok=1NoW3aI6)
$6^2 - 5^2 = 36-25=11$
$\therefore$ thrid side is $\sqrt{11}$
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![Right Angled Possibilities Right Angled Possibilities](/sites/default/files/styles/large/public/thumbnails/content-id-5025-right%252520angled%252520possibilities%2525203.png?itok=_74Z_6P2)
Impossible since the hypotenuse should be the longest side
$\therefore$ there are only 2 possibilities.