Question

Using Pythagoras theorem determine the length of AD in terms of b and c shown in the given figure.

Answer 1

In ∆ABC and ∆DBA,

(90º each)

(Common)

Therefore, by AA-criterion for similarity, we have .

Now we will substitute the values of AC and AB

We are finding the value of AD therefore; we will use the following ratios,

Now we will multiple both sides of the equation by .

We will simplify the above equation as below,

..…(1)

But we know that substituting the value of BC in equation (1) we get,

Therefore, the value of AD in terms of b and c is.