We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

This is just a fun question:

Prove a 45-45-90 triangle has side ratios \(1:1:\sqrt2\) WITHOUT Pythagorean Theorem or Trigonometry.

Can you do it?

(also, I'm kind of curious because I don't know how to prove it without Pythag. or Trig, is it even possible?)

:P

CoolStuffYT Dec 13, 2018

#1**+3 **

Sure, it's possible by considering the area. We can assume that the legs have a length 1 and so we wish to find the length of the hypothenuse which we will call x. The area then becomes \(\frac{1}{2}\). If we draw the height of the triangle from the hypothenuse we notice that it has the length \(\frac{x}{2} \) and so the area can also be calculated to be \(\frac{x \cdot \frac{x}{2}}{2}\). We then get the equation \(\frac{x^2}{4}=\frac{1}{2} \) or \(x^2=2\) and so \(x= \sqrt{2}\) and the ratio is \(1:1:\sqrt{2}\)

.Guest Dec 13, 2018