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):
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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