Question

:( can someone help me....I don't understand this question... Please help

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse.

30 and 40
15 and 36
70 and 250
45 and 51
15 and 20
96 and 100

Answer 1

so you are being asked if these 2 sides of a right triangle are part of a triangle that has a hypotenuse that is a whole number

as an example..

pythagoras' theorem is basically

\[a^2 + b^2 = c^2\]

so a right triangle with shorter sides 5 and 12... will the hypotenuse be an integer of whole number

then

\[c^2 = 5^2 + 12^2~~~so~~~c^2 = 25 + 144 ~~~~~c^2 = 169\]

now take the square root of both sides to find c, the hypotenuse

\[c = \sqrt{169} ~~~~~~c = 13\]

so right triangle with sides 5, 12 and 13 meets the rule set in the question.

hope it helps

Answer 2

That helps a lot. How do i figure out if it is a leg or hypotenuse though?

Answer 3

@campbell_st

Answer 4

well you may need 2 calculations.... I looked at the question and read it as you were given the shorter legs...

the alternative is to use subtraction

\[b^2 = c^2 - a^2\]

c is the larger of the pair...a is the smaller

the 1st and 2nd last will need to adding version