Answer:
[tex]b=3\sqrt{13}[/tex]
Step-by-step explanation:
In a right angled triangle, if a perpendicular is drawn from a vertex of the right angle then triangles on both sides of the perpendicular are similar.
In ΔPDY, ∠D = 90° and DM ⊥ PY
So, ΔPMD ≈ ΔDMY
If two triangles are similar then their corresponding sides are proportional.
[tex]\frac{PM}{DM}=\frac{MD}{MY}[/tex]
Put [tex]PM=4\,,\,DM=c\,,\,MD=c\,,\,MY=9[/tex]
So,
[tex]\frac{4}{c}=\frac{c}{9}\\\\c=36\\c=6[/tex]
According to Pythagoras theorem, square of hypotenuse is equal to sum of squares of the other two sides.
In ΔDMY,
[tex]DY^2=DM^2+MY^2\\b^2=c^2+9^2[/tex]
Put [tex]c=6[/tex]
[tex]b^2=6^2+9^2\\b^2=36+81\\b^2=117\\b=\sqrt{3^2(13)}\\b=3\sqrt{13}[/tex]
