Question

Dawn is trying to find the dimensions of a parallelogram. She knows that the base is one unit less than twice the height of the shape. The area is 91 square units. How long are the base and height?

Answer 1

Let x = the height.
Then the base would be 2x - 1

The area of a parallelogram is shown by the formula
A = bh

So, plugging in for the area, the base, and the height...

91 = (2x-1) x

Now we have to solve for x.
Distribute
91 = 2x^2 - x

Set equal to 0.
0 = 2x^2 - x - 91

Now factor...
You may want to review "factoring quadratics."
The challenge is to find factors of 91 that can combine to -1 when one if multiplied by 2.
13 times 7 is 91.
If the 7 is multiplied by 2, we get 14 which is one away from the 13.
So, the factored form is...

0 = (2x + 13) (x-7)

Now to find the solutions for x, set each factor equal to 0.

2x + 13 = 0
2x = -13
x = -13 / 2

And

x - 7 = 0
x = 7

So there are two answers for x... 7 and negative 13/2
In this problem, the length of the height cannot be negative, so the only answer that makes sense is 7.

The height (x) is equal to 7.

Now, recall that the base is 2x - 1.
Since x is 7, the base is 2 (7) - 1
Or
14 - 1
Which is 13.

So the base and height are 13 and 7 respectively (in that order).