Question

What is the length of the hypotenuse of 45–45-90 triangle with legs of length 5 square root 3

Answer 1

Length of hypotenuse (h) of 45-45-90 triangle with legs = 5sr3
The legs of a 45-45-90 triangle are equal since their opposite angles (45) are equal. The ratios for the sides of all 45-45-90 triangles is:
x, x, xsr2
$x \: across \: the \: 45s \: and \: x \sqrt{2} for \: h \\ so \: make \: x = 5 \sqrt{3}$
$then \: h = x \sqrt{2} = 5 \sqrt{3} \times \sqrt{2} \\ h = 5 \sqrt{3 \times 2} = 5 \sqrt{6}$