Consider triangle def. the legs have a length of 36 units each.

triangle d e f is shown. angle d f e is 90 degrees and angles f d e and d e f are 45 degrees. the lengths of sides d f and f e are 36 units.

what is the length of the hypotenuse of the triangle

18 units
18 startroot 2 endroot units
36 units
36 startroot 2 endroot units

36 StartRoot 2 EndRoot units

Step-by-step explanation:

The triangle DEF can be sketched where the base is FE , height is DF and the hypotenuse is DE. Side  FE which is the base contains angle F 90°.Side DF=FE=36 units.Angles FDE=DEF=45°.

Hence triangle DEF is a right-isosceles triangle with sides 36 units.To find the hypotenuse you apply the Pythagorean relationship where the sum of squares of the two sides equals the square of the hypotenuse.

This means;

36²+36²=c²  where c is the hypotenuse

1296+1296=c²

2592=c²

√2592=c

√32 × √81 =c

√2 × √16 × 9 =c

√2 × 4×9 =c

36√2 = c