The base of a triangle is seven less than twice its height. if the area of the triangle is 100cm^2 find the length of the base explain this too me i'm stuck

h≈4.874 cm,b≈21.748 cm

Atriangle=12bh

"The base of a triangle is twelve more than twice its height."

From this we can say that:

b=2h+12

So, if A=12bh, we can replace b with 2h+12.

A=12(2h+12)h

53=12(2h+12)h

53=(h+6)h

53=h2+6h

h2+6h−53=0

Use the quadratic formula.

h=−6±√62−4(−53)(1)2

h≈4.874

(Ignore the negative answer—height can't be negative.)

b≈2(4.874)+12

b≈21.748

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

50.6

step-by-step explanation: