Question

If the hypotenuse of a 45º-45º-90º triangle is 54 inches long, what is the length of one of the legs? Leave your answer in radical form.
27 square root of 2 inches
54 square root of 2
Square root of 2
27

and can you tell me how to do this

Answer 1

This is a right angled triangle and we can use Pythagorus' Theorem. And more than that, this is an isoceles triangle, so the two non-hypothenuse side lengths are the same. Call them X

So X^2 + X^2 = 54^2

Now solve for X

Answer 2

27?

Answer 3

Let's test. If X = 27, then

X^2 + X^2 = 2 . 27^2

But that is not equal to 54^2, because 54^2 = 2^2 . 27^2

Answer 4

So no, 27 is wrong. Do the algebra and don't guess.

Answer 5

27sqrt2?

Answer 6

What did the algebra tell you?

Answer 7

\[X^2 = (27\sqrt{2})^2 = 2 \times 27^2\]
so\[X^2 + X^2 = 4 \times 27^2 = 2^2 \times 27^2 = (2 \times 27)^2 = 54^2\]
Hence yes, 27.sqrt(2) is correct.