SOLUTION: Area= 105cm^2; it's height is 8 more than it's base....find the height and base?

Question 837525: Area= 105cm^2; it's height is 8 more than it's base....find the height and base?
Found 2 solutions by Alan3354, josh_jordan:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find a pair of factors of 105 that differ by 8.
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it's = it is

Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
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.
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