The hypotenuse of a 45°-45°-90° triangle measures 128 cm. A right triangle is shown. The length of the hypotenuse is 128 centimeters and the lengths of the other 2 sides are congruent. What is the length of one leg of the triangle? 64 cm 64 StartRoot 2 EndRoot cm 128 cm 128 StartRoot 2 EndRoot cm

64√2 or 64 StartRoot 2 EndRoot

Step-by-step explanation:

A 45-45-90 traingle is a special traingle.  Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem.  Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2.  2(x)^2=c^2.  You then square root both sides and get c= x√2.  

Therefore, the two legs are x and the hypotenuse is x√2.  x√2=128 because the question says that the hypotenuse is 128.  Solve for x by dividing both sides by √2.  X=128/√2.  You rationalize it by multiplying the numberator and denominator of the fraction by √2.  √2*√2= 2.

X=(128√2)/2= 64√2 cm.

Since X is the leg, the answer would be 64√2

98 points djdjsi zisksis sjsjsi sisksj sksjdj sksks sjsisj