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Finding Pythagorean Triplets for Any Given Number

Triangle XY...

Question

Triangle $X Y Z$ is right-angled at vertex $Z$ . Calculate the length of $Y Z$ , if $X Y = 13$ and $X Z = 12$

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Solution

$△ X Y Z$ is a right angled triangle

By Pythagoras Theorem,

${X Y}^{2} = {Y Z}^{2} + {X Z}^{2}$

$13^{2} = {Y Z}^{2} + 12^{2}$

$169 - 144 = 25 = {Y Z}^{2}$

$Y Z = \sqrt{25} = 5 u n i t s$

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