The perimeter of the given triangle is

~73.68

Step-by-step explanation:

In the right triangle with one angle = 45 deg

=> Isosceles right triangle

=> a = b = hypotenuse/sqrt(2) = (12sqrt(2))/sqrt(2) = 12

In other right triangle with 3 sides are a, c, and d, we have:

sin (30 deg) = a/d

=> d = a/sin(30 deg) = 12/(1/2) = 12 x 2 = 24

Othwise, cosine (30 deg) = c/d

=> c = d x cos(30 deg) = 24 x sqrt(3)/2 = 12sqrt(3)

=> The perimeter of the biggest triangle is calculated by:

P = 12sqrt(2) + b + c + d = 12sqrt(2) + 12 + 12sqrt(3) + 24 = ~73.68

Hope this helps!

0.43.

Step-by-step explanation:

The probability that the customer will pay with debit card = 50%

The percentage of customers who use coupons 30% and  35% pay with debit card.

Now calculate the probability  that the same person will use coupon:

P[Uses coupons | Pays with Debit card] = P[Uses coupons and pays with debit card] / P[ Pays with debit card]

= 0.3 * 0.5 / 0.35

= 3/7  or  0.4286 or 42.86%