Calculate the length of the unknown side for the given triangle

Question

safia21 · Answer

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anonymous · Answer

I think this is similar to the problem safia solved for you in the pdf

anonymous · Answer

But all the same I'll give you my explanation. You have two sides and you need to find the unknown side of the right triangle so the formula you will use is Pythagoras theorem

anonymous · Answer

$$a ^{2}+ b ^{2}+ = c ^{2}; a = 12, b = 18, c = ?$$

jim_thompson5910 · Answer

$$\large a^2+b^2=c^2$$


$$\large 12^2+18^2=c^2$$


$$\large 144+324=c^2$$


$$\large 468=c^2$$


$$\large c^2=468$$


$$\large c=\sqrt{468}$$


$$\large c=\sqrt{4*117}$$


$$\large c=\sqrt{4}*\sqrt{117}$$


$$\large c=2\sqrt{117}$$


$$\large c \approx 21.63330765$$
So the unknown side is roughly 21.63330765 units

jim_thompson5910 · Answer

oops, you can simplify further to get $$\large c=6\sqrt{13}$$, which is the exact length.

anonymous · Answer

$$c ^{2} = 18^{2}+12^{2}= 468$$

anonymous · Answer

Because c is being squared we take the inverse of that which is the square root. So we take the square root of both sides so that we are left with just c on the left side:
$$c = \sqrt{468} = \sqrt{2\times234} = \sqrt{4\times117} = \sqrt{4\times9\times13} = 6\sqrt{13}$$