Is a triangle with sides of lengths 24, 70 and 74 a right triangle?

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Is a triangle with sides of lengths 24, 70 and 74 a right triangle?

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Answer 1 · 2015-11-14T00:03:29

Yes

Explanation:

$24^2+70^2=576+4900=5476=74^2$

So these side lengths satisfy Pythagoras Theorem.

An alternative way of approaching this might be as follows:

$24$ , $70$ and $74$ are all divisible by $2$ , so this triangle is a right angled triangle if and only if a triangle with sides $12$ , $35$ and $37$ is a right angled triangle.

Notice that $35 = 6^2-1$ , $37 = 6^2+1$ and $12 = 2*6$ . This looks like a pattern we could check:

$(a^2-1)^2 = a^4-2a^2+1$

$(a^2+1)^2 = a^4+2a^2+1$

$(2a)^2 = 4a^2$

So:

$(a^2+1)^2 = a^4+2a^2+1 = a^4-2a^2+1+4a^2 = (a^2-1)^2+(2a)^2$

In our case $a=6$ , but any number $a$ would work.

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Is a triangle with sides of lengths 24, 70 and 74 a right triangle?

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Explanation:

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