Question

1

The base of a parallelogram has a length of x meters, and the height of the parallelogram is x - 1
meters. The parallelogram has an area of 306 square meters. What is the value of x?
9
17
18
34

Answer 1

The area of a parallelogram is given by the formula A = base x height. In this case, the base has a length of x meters, and the height is x - 1 meters. So we can write:

A = x(x - 1)

We are told that the area is 306 square meters, so we can set up an equation:

x(x - 1) = 306

Expanding the left side gives:

x^2 - x = 306

Bringing all the terms to one side gives a quadratic equation:

x^2 - x - 306 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = -1, and c = -306, so:

x = (1 ± sqrt(1 - 4(1)(-306))) / 2(1)

x = (1 ± sqrt(1 + 1224)) / 2

x = (1 ± sqrt(1225)) / 2

x = (1 ± 35) / 2

So x is either (1 + 35) / 2 = 18 or (1 - 35) / 2 = -17/2. Since x represents a length, it cannot be negative, so the value of x is 18 meters.

Therefore, the answer is x = 18.