Question

In an isosceles right triangle, the hypotenuse is 15 units, what is the measurement of one leg?

Answer 1

`(15sqrt2)/2` units

Explanation:

An isosceles right triangle, is always a 45-45-90 degrees triangle, therefore:
Side opposite to 90 degrees: `xsqrt2`
Side opposite to 45 degrees: `x`
Side opposite to 45 degrees: `x`

And since the hypotenuse is 15:
`xsqrt2=15`
`x=15/sqrt2*sqrt2/sqrt2= (15sqrt2)/2`

Answer 2

A leg would be `approx 10.61` units

Explanation:

We know that Pythagorean Theorem is `a^2+b^2=c^2`. And since this is an isosceles right triangle, we know that `a` and `b` are equal. (This is because in an isosceles right triangle, the two legs are equal...like below)

Lets replace `a` and `b` for x (since they are equal)

`a^2+b^2=c^2`

`x^2+x^2=c^2`

`x^2+x^2=15^2`

`2x^2=225`

Now you can divide both sides by two.

`(2x^2)/2=15/2`

`x^2=112.5`

Now square root both sides for your answer...

`sqrt(x^2)=sqrt(112.5)`

`x=2.7386127875258`

Round this to the nearest hundredth...

`xapprox10.61`