Triangle ABC:
<ABC=90°
<ACB=y
Triangle CDE:
<CDE=90°
<DCE=y
The two triangles have two congruent angles, then they are similars, and theirs sides must be proportionals:
Adjacent angle to y / Hypotenuse
Triangle CDE Triangle ABC
CD/CE = BC/AC
Replacing the values:
x/7=(20-x)/21
Solving for x. Cross multiplication:
(21)(x)=(7)(20-x)
21x=140-7x
21x+7x=140-7x+7x
28x=140
28x/28=140/28
x=5
Length of CD = x = 5
Answer: The length of CD is 5
Answer: 5
