In the diagram abc=adb=90, ad=p and dc=q. use similar triangles to show that x2=pz plzz anyoneee

By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that

Step-by-step explanation:

Given that ∠ABC=∠ADC, AD=p and DC=q.

Let us take compare Δ ABC and  Δ ADB in the attached file , ∠A is common in both triangles

                                                                     and given ∠ABC=∠ADB=90°

Hence using AA postulate, ΔABC ≈ ΔADB.

Now we will equate respective side ratios in both triangles.

Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.

Cross multiply

Hence proved.

-5 < a - 4 < 2

solving for a

a - 4 > - 5

a >  -1    and

a - 4 < 2

a < 6

So the correct solution set is the third one.