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if sides a and b are 100m, and there is a right angle, then how long is side c?. By the way, I made it on paint quickly.

>--triangle link<--

I AM ONLY A 6TH GRADER SO PLEASE DO NOT PUT THINGS LIKE "Pythagorean theorem" AND "100√2" BECAUSE I WILL NOT UNDERSTAND

Awesome Gamer 333
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3 Answers3

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I get $100\sqrt2$ with the Pythagorean theorem.

  • can you please explain that more clearly? I am only a 6th grader and have trouble understanding. – Awesome Gamer 333 Jan 31 '19 at 02:17
  • I drew a right triangle and called two sides $x$, the other $c$. Then the Pythagorean theorem says $2x^2=c^2$. Hence $c=\sqrt2 x$. Finally, $x=100$. –  Jan 31 '19 at 02:20
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To find the third side of a right triangle given two of them, you can use the Pythagorean Theorem given by: $$a^2+b^2=c^2$$

Note that $c$ is the hypotenuse and $a$ and $b$ are the legs.

Your drawing indicates that you have the two legs so you can plug the values into the formula to find $c$.

$$(100)^2+(100)^2=c^2$$

$$10000+10000=c^2$$

$$c^2=20000$$

$$c=\sqrt{20000}$$ $$c=100\sqrt{2}$$

Just make sure you include meters as a unit.

I hope this helps, if you need any explanation of how I progressed between steps, let me know in the comments.

Gnumbertester
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It is nice that you included a picture, but I would figure out that c is the hypotenuse anyway, as the hypotenuse is always longer than the other 2 sides. This is using the Pythagorean theorem.

To see this better you need to know the Pythagorean theorem:

Here is one shape that can be used to prove the theorem

You will see there that the assigned value for the hypotenuse of one of the 4 congruent triangles is c (and so will be the same for the others).

You should try using this to prove the theorem to figure out that $a^2+b^2=c^2$ where c is the hypotenuse (identifying the hypotenuse is important as it may not always be c).

In case you need a hint, but only after trying should you see the hint: try calculating the whole area in 2 different ways.

Then you can find the side c of your triangle by using the Pythagorean theorem. It's $100\sqrt2$, which should agree with your answer.

Mafematician
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