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# geo met ry halp

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Without using a calculator, find the hypotenuse of a right triangle that has legs with lengths  and .

for the extra challange you dont have to but if you want to use a calculator you can.

P.S. Since im looking fo a quick answer you dont have to write the explanation, but again if you want to you can.

Guest Oct 28, 2017
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#1
+5229
+2

How are you going to know how to do these on a test if you don't know the explanation??

We can use the Pythagorean theorem to do this problem. The Pythagorean theorem says

a2 + b2  =  c2      , where  " a "  and  " b "  are legs of a right triangle, and  " c " is the hypotenuse.

They tell us the legs are  264  and  495  .   So...

2642 + 4952  =  c2              Multiply  264 * 264  to get  69,696  and  495 * 495  to get  245,025 .

69,696 + 245,025  =  c2     Add them

314,721  =  c2                    Take the positive square root of both sides.

561  =  c

hectictar  Oct 28, 2017
edited by hectictar  Oct 28, 2017
#2
+1364
+2

Well, if I was truly not allowed to use a calculator during any step throughout this problem, I would do the following:

\(264^2=(200+60+4)(200+60+4)=200(200+60+4)+60(200+60+4)+4(200+60+4)\)

There are a lot of friendly numbers here, do you agree? Now, let's continue the expansion.

\(200(200+60+4)+60(200+60+4)+4(200+60+4)=40000+12000+800+12000+3600+240+800+240+16\)

WOAH! That's a lot of terms! I would first rearrange the numbers such that the largest are added to the smallest.

\(40000+12000+12000+3600+800+800+240+240+16\)

You can do addition in any order you'd like. The colors indicate an addition where the result will be friendly and will end in another 0.

\(40000+12000+12000+3600+800+800+240+240+16=69696\)

I wouldn't do 495 the same way, however. I would break that into \((500-5)(500-5)\). Now, do the same thing like before.

\(500(500-5)-5(500-5)\)

\(250000-2500-2500+25\)

\(245025\)

The square root is where I would hit a barrier, though...

TheXSquaredFactor  Oct 28, 2017
#3
+78590
+3

Note that   264  /  495  =    8  / 15

So......the ratio of the legs  is   8  :  15

And one of the Pythagorean "Triples"  is     8  : 15  : 17

So.........

264 / 8  =  33

And the hypotenuse must be......17 * 33  =   561

So......the  sides are    264 -  495  - 561

CPhill  Oct 29, 2017

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