Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.

check the picture below

and isosceles triangle, has two equal sides, thus, sides "a" and "b" for the triangle to be an isosceles, have to be equal

The length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length is; 1.414 units

we have;

Lengths of 2 legs as;

x = 1

y = 1

Hypotenuse length is;

h = √(1² + 1²)

h = √2

h = 1.414 units

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step-by-step explanation:

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584