# of a right triangle has a hypotenuse (slant) of square root of 52, how do you find the lengths of the legs?

Update:

it only tells me the hyptenuse. im not sure if the legs are equal..HELP

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Is it isosceles (with the legs the same length)?

Then you can solve using:

a² + b² = c²

c² = sqrt(52)² = 52

Thus a² + b² = 52

If a = b, then a² = 26

a = b = sqrt(26)

Otherwise, if you don't have some other information, you can't uniquely solve for the length of the legs. The legs could have lengths from nearly 0 to nearly sqrt(52).

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• you can't. you need more information. The legs could be the same size, or two different sizes. I can tell you that if they are the same length, the legs would be the square root of 26. As long as both legs squared equal the square root of 52 its a possible answer. Pythagorean theorem, A squared, plus B squared, equals C squared. Where A and B are the legs, and C is the hypotenuse.

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• Anonymous

A Squared Plus B Squared Equalls Hypotenuse Squared..

So in a right angled triangle with legs of A 3 units & B 4 units

3X3=9 4X4=16 9+16=25 Sqare root of 25 = 5

So the hypotenuse is 5 units..

If you have hypotenuse of square root 52

you need to know the lenght of one of the legs to work out the lenght of the other....

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• this is not a theorem: - "in a stunning angled triangle the size of the hypotenuse=sq. root ( sq. of adjacent + sq. of opposite area)" however the Pythagoras theorem is used in such way. learn Pythagoras theorem and your confusion would be cleared.

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• If you are looking for integer solutions, a^ + b^2 = 52

16 + 36 = 52

a = 4

b = 6

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• Are the legs equal?

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• Use the Pythagorean Theorem. If you tell us one leg, we'll help you find the other

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• does it say the sides are integers perhaps? otherwise you can't determine the lengths based on the information you have given

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• not enough info.

if they're equal length then they are both sqr(26)

If they're whole numbers they are 4 and 6

could be anything.

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