1. The length of the hypotenuse of a 45°-45°-90° triangle is 16 cm. What is the length of each leg?

Answer 1

draw a diagram

in a 45-45-90 right triangle the legs are congruent; you have an isosceles right triangle

in a 45-45-90 right triangle the hypotenuse is equal to the length of one of the congruent legs multiplied by

√2, so if "n" is the length of one of the legs, then the hypotenuse is n√2

the hypotenuse is 16 cm

16=n√2

n=16/√2

n=16√2/2

n=8√2 cm, or 8*1.4142136=11.313708 cm is the length of each leg

you can also use the Pythagorean Theorem

n^2+n^2=16^2

2n^2=256

n^2=128

take the square root of each side

n=√128

n=11.313708 cm again

Answer 2