Question

In the figure below a surveyor put stakes at the lettered points. He used string to determine lengths of line segments and to check that lines ACE and BCD form right angles at C.

If DC = 12 , CE = 16, DE = 20 and DB = 60 and CE/CB = DC/AC = DE/AB.
How long is CB?
What is the ratio of CE to CB in lowest terms?
What will be the length of AC?
What will be the length of AB

Answer 1

30

Explanation:

Answer 2

CB=48; CE/CB = 1/3; AC=36; AB=60.

DB=DC+CB
60=12+CB

Subtracting 12 from both sides,
60-12=CB
48=CB

The ratio of CE/CB would then be 16/48 = 1/3.

Using this ratio to find AC,
1/3 = 12/AC

Cross multiply:
1*AC = 3*12
AC = 36

Using the ratio of CE/CB to find AB,
1/3 = 20/AB
1*AB = 3*20
AB=60