Question 837525
First, we need to know the formula for finding the area of a parallelogram, which is:  A = bh


We are told that the height is 8 more cm than the base.  In other words, 


h = 8 + b


Next, will replace h with 8 + b in our formula for the area of a parallelogram:


A = b(8 + b)


Since we are told the area is 105, we will replace A with 105:


105 = b(8+b)


Next, we will multiply b by everything inside the parenthesis, giving us:


105 = 8b + b^2


We need to solve for b, so we can subtract 105 from both sides of our equal sign, which will give us a quadratic equation:


0 = 8b + b^2 - 105


Let's rewrite our equation and put it into standard form:


b^2 + 8b - 105 = 0


We can see if we can factor this equation by seeing if there are 2 factors of -105 that can be multiplied together to give us -105 and added together to give us 8.  There are:  15 and -7.  In factored form, we have:


(b + 15)(b - 7) = 0, giving us


b = -15 and 7.


Since the side of a parallelogram cannot be negative, our base will equal 7.  To find our height, replace h with 7 in equation h = 8 + b (as shown above):


h = 8 + 7 which gives us


h = 15


Therefore, the base is 7 cm and the height is 15 cm.