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Answer:

76 units

Step-by-step explanation:

In the given figure, a circle with center Q is inscribed in triangle AHD.

Let the circle with center Q touches the side HD at point N.

So, AT & AM, DM & DN and HT & HN are tangents drawn from external points A, D and H respectively.

Since, measure of tangsnts drawn from external point to a circle are equal.

Therefore,

AM = AT = 18

HN = HT = 8

DM = DN = 12

AH = AT + HT = 18 + 8 = 26

AD = AM + DM = 18 + 12 = 30

HD = DN + HN = 12 + 8 = 20

Perimeter of triangle

= AH + AD + HD

= 26 + 30 + 20

= 76 units

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