Multiple choice

If the perimeter of a right-angled isosceles triangle is $ \displaystyle \sqrt{2}+1$, then what is the length of the hypotenuse?

  1. $\dfrac{1}{\sqrt2}$ cm
  2. $\sqrt2$ cm
  3. $1$ cm
  4. $2$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the sides be x, x, and hypotenuse h = x*sqrt(2). Perimeter = 2x + x*sqrt(2) = x(2+sqrt(2)) = sqrt(2)+1. x = (sqrt(2)+1) / (2+sqrt(2)) = (sqrt(2)+1) / (sqrt(2)*(sqrt(2)+1)) = 1/sqrt(2). Hypotenuse = x*sqrt(2) = (1/sqrt(2)) * sqrt(2) = 1.

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