The base of a rectangle is 2cm greater than its height. Find the base and the height of the parallelogram if the area of the parallelogram is 120 cm2. Can this be shown as a quadratic and factored?
b = h+2
bh = 120
(h+2)h = 120
h^2 + 2 h - 120 = 0
(h-10)(h+12) = 0
h = 10
b = 12
To find the base and height of the parallelogram, let's assume that the height of the parallelogram is x cm.
According to the given information, the base of the rectangle is 2 cm greater than the height. Therefore, the base can be represented as (x + 2) cm.
The area of a parallelogram is given by the formula: Area = base * height. Substituting the values, we have:
120 cm2 = (x + 2) cm * x cm
To check if this equation can be shown as a quadratic and factored, let's simplify it:
120 = x^2 + 2x
Rearranging the equation to the standard quadratic form:
x^2 + 2x - 120 = 0
Now it is in the form of a quadratic equation. To factor it, we need to find two numbers that multiply to give -120 and add up to 2.
The factors of -120 that add up to 2 are 12 and -10:
(x + 12)(x - 10) = 0
Setting each factor equal to zero:
x + 12 = 0 and x - 10 = 0
Solving for x, we get:
x = -12 and x = 10
Since the height cannot be negative, we discard the value x = -12.
Therefore, the height of the parallelogram is x = 10 cm.
Substituting this value back into the equation for the base:
Base = x + 2 = 10 + 2 = 12 cm
So, the base of the parallelogram is 12 cm, and the height is 10 cm.
In conclusion, the base and height of the parallelogram are 12 cm and 10 cm, respectively.