How Do you find the length and width of a triangle with just the hypotenuse?

Question

Im doing a project for school, where we have to find how much a tv costs per square inch of screen, and we were supposed to use the size to figure out the length and width, but I had cant seem to figure out how to do it, no matter how many times I read the information our teacher gave us.
If its a^2+b^2=c^2 and C= 50, how could you figure out the rest of the information??

Answer 1

well... not possible unless u know aspect ratio of tv. (no, tvs arent squares) if we assume that the aspect ratio of the tv is the standard 4:3, then do (3x)^2+(4x)^2=50^2, where 3x=a and 4x=b.
then (3x)^2+(4x)^2=2500
then 9x^2+16x^2=2500
then 25x^2=2500
then 5x=50
then x=10
so, a=30 and b=40

wait.... THIS IS A 3,4,5 TRIANGLE!!!!!!!!!!!!!!!!!!!!!!!!! the most basic of all pythagoreans.

Answer 2

First of all, no TV is square, so you can throw that answer out.

All TVs are rectangular, and as it turns out (at least pre-HD) they all have the same aspect ratio -- that is, the ratio between the height and the width. It has to be the same because standard video images are all the same height and width.

Specifically, TVs follow this very special relationship: 3 units high, 4 units wide, which yields a diagonal of 5 units. The ancient Greeks used this 3:4:5 triangle as the basis for a lot of their architecture, as it's a special kind of symmetry that the eye finds very pleasing; the Egyptians used it in elements of the Great Pyramid of Giza. And it was adopted as the basis for TV screens and video monitors (again, before the invention of HDTV and 16:9 screens... and yet even those are 4 x 4 and 3 x 3, yes?)

So in this case... 30 x 30 is 900, 40 x 40 is 1600, and 900 + 1600 is 2500... for which the square root is 50.

Now, if you didn't know the magic 3 x 4 x 5 ratio, could you have figured this out by yourself? Probably, with a little thinking. What you could have done was take c^2, which is 2500, and then look for two numbers that add up to 2500, are NOT equal (because NO television screen is square), AND are squares themselves. 900 and 1600 are the obvious choices, because they're so easy. (Sometimes life just works out like that. :-)

And by the way, the next time somebody asks you the difference between mathematics and arithmetic... knowing that 50 times 50 equals 2500 is arithmetic. Knowing that you need to look for two different numbers, both squares, that add up to 2500 is mathematics.

Live long and prosper! :-)

Answer 3

In a practical sense (if you only want to estimate) the area of the TV would be a little less than half the hypotenuse squared (h*h/2) where h is the hypotenuse. The exact formula would be:

hypotenuse * hypotenuse * .48 = area of the triangle

You can't find the width & height since that could vary and still give the same hypotenuse.

Answer 4

If side a=side b then a=b and you can say 2a^2=2500
a^2=1250
a= sq.root of 1250 which is = to sq. root of 625 x 2
a=25 times sq. root of 2

This is only if sides a & b are equal. If they are not, then I do not think you can.

With this in mind, with a hypotenuse of 50 inches, then each of the 4 sides will be 35.355 inches long. Then compute the surface area of the screen which is 35.355 x 35.355=1249.9 or 1250 sq. inches. If the tv costs $500 then the cost per sq inch is 500 divided by 1250= .40

Answer 5

that has nothing to do with the hypotenuse, just multiply the length times the width of the screen and do the following equation: cost of tv ÷ area of screen (lenght x width) and there's your answer :)

Answer 6

Are you sure there aren't any other hints? Maybe it says a square TV? Sometimes math problems do that.

Answer 7

most T.V's are square...if that's the case, then a=b...so really
2a^2=50^2
a^2=1250
a=35.355

if it isn't a square...then you might have to do something weird, and I wouldn't know how to do that, unless you had some angles to give me.

Answer 8

Ask your teacher about the Pythagorian Theorm. a2+b2=c2

Answer 9

Wow, i need more than the value of C to find that out.

Answer 10

you would have to know at least one more leg. make sure u have done evrything to find the other legs, because you have to know at least two of the legs to find out the thrid.