Question

in the diagram below DE is parallel to AB if DE is 10 less than CE,CB=48 and AB =32, find the length of CE. figures are not necessarily drawn to scale. star your answer in simplest radical form, if necessary

Answer 1

The length of CE is found to be approximately 36.5714 units by setting up a proportion using the properties of similar triangles where DE is parallel to AB, and substituting the given values of AB and CB.

Step-by-step explanation:

To find the length of CE in the diagram, where DE is parallel to AB, DE is 10 less than CE, CB is 48, and AB is 32, we can use the properties of similar triangles.

Since DE is parallel to AB, triangle CDE is similar to triangle CAB. We can set up a proportion where AB/BC = DE/CE since corresponding sides of similar triangles are proportional.

Substituting the given values into the proportion, we have:

32/48 = (CE - 10)/CE

CE = 48 * 32 / (32 + 10)

CE = 1536 / 42

CE = 36.5714

Thus, the length of CE is approximately 36.5714 units, which is the simplest form since no radical was necessary in this case.