SOLUTION: In right triangle ABC, CD is the altitude drawn to hypotenuse AB. AD is 2 units less than DB, and CD=3. In this triangle, which statement is true: 1) CD is less than DB 2) CD i

Algebra ->  Triangles -> SOLUTION: In right triangle ABC, CD is the altitude drawn to hypotenuse AB. AD is 2 units less than DB, and CD=3. In this triangle, which statement is true: 1) CD is less than DB 2) CD i      Log On


   

Question 421332: In right triangle ABC, CD is the altitude drawn to hypotenuse AB. AD is 2 units less than DB, and CD=3. In this triangle, which statement is true:
1) CD is less than DB
2) CD is equal to DB
3) CD is greater than DB
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!





Right triangles ABC, ACD, and CBD are all similar.

Therefore since ACD and CBD are similar,

      x - 2     3
     ——————— = ———
        3       x

Cross multiply:

    (x - 2)x = 3*3
 
     x² - 2x = 9

 x² - 2x - 9 = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%282+%2B-+sqrt%284%2B36+%29%29%2F%282%2A%281%29%29+

x+=+%282+%2B-+sqrt%2840%29%29%2F2+

x+=+%282+%2B-+sqrt%284%2A10%29%29%2F2+

x+=+%282+%2B-+2sqrt%2810%29%29%2F2+

x+=+%282%281+%2B-+sqrt%2810%29%29%29%2F2+

x+=+%28cross%282%29%281+%2B-+sqrt%2810%29%29%29%2Fcross%282%29+

x+=+1+%2B-+sqrt%2810%29+

So DB has length 1%2Bsqrt%2810%29 or about 4.162

CD is given to be 3, so since 3 is less than DB, which is 4.162.

Therefore CD is less than DB, choice 1)

Edwin