Answer: [tex]P\triangle ADH = (a+b+\sqrt{a^2+b^2} )[/tex] unit
Step-by-step explanation:
Since Here Δ ABC is a isosceles triangle.
Also, [tex]AH\perp BC[/tex] and [tex]HD\perp AC[/tex]
Thus, ∠ ADH = 90°
That is, Δ ADH is the right angle triangle.
In which, AD = a unit and HD = b unit
And, By the definition of Pythagoras theorem,
[tex]AH^2 = HD^2 + AD^2[/tex]
⇒ [tex]AH^2 = a^2 +b^2[/tex]
⇒ [tex]AH = \sqrt{a^2+b^2}[/tex]
Since, the perimeter of a triangle = sum of the all sides of the triangle.
Therefore, perimeter of ΔADH = AD + DH + AH
= [tex]a + b + \sqrt{a^2+b^2}[/tex] unit
