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 triangle18 units18 StartRoot 2 EndRoot units36 units36 StartRoot 2 EndRoot units

Answer:36 StartRoot 2 EndRoot unitsStep-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 hypotenuse1296+1296=c²2592=c²√2592=c√32 × √81 =c√2 × √16 × 9 =c√2 × 4×9 =c36√2 = c