Question

How do you find the length of each leg of an isosceles right triangle whose hypotenuse is 14 cm?

Answer 1

`14/sqrt2=7sqrt2`

Explanation:

An isosceles right triangle is a right triangle with two legs equal in length and has angles of `45^@-45^@-90^@`.

By Pythagorean Theorem, we know that,
hypotenuse `c^2=a^2+a^2, => c=asqrt2`
where `c` is the hypotenuse and `a` is the leg.

So for an isosceles right triangle with side length `a`, the hypotenuse has a length of `asqrt2`.

Similarly, if the hypotenuse of an isosceles right triangle has length of `a`, the legs have a length of `a/sqrt2 or (asqrt2)/2` each.

Given that the hypotenuse of the isosceles right triangle `=14`,
`=>` the length of each leg `=14/sqrt2=7sqrt2`

Check : `(7sqrt2)^2+(7sqrt2)^2=196=14^2` (OK)