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

To find the dimensions of the parallelogram, we can set up equations based on the given information. The height of the parallelogram is approximately 6.438 units, and the base is approximately 11.876 units.

Step-by-step explanation:

To solve this problem, we need to set up equations based on the given information. Let's denote the height of the parallelogram as 'h' and the base as 'b'. The problem states that the base is one unit less than twice the height, so we can write the equation: b = 2h - 1. The area of a parallelogram is given by the formula A = base x height. Substituting the values we have, 91 = (2h - 1) x h.

Now we can solve this quadratic equation to find the height. Rearranging it, we have 2h^2 - h - 91 = 0. Factoring or using the quadratic formula, we find that the roots are h ≈ -6.688 and h ≈ 6.438. Since the height cannot be negative, we can discard the negative root. Thus, the height of the parallelogram is approximately 6.438 units.

To find the base, we can substitute the height value into the equation b = 2h - 1. Plugging in h = 6.438, we get b ≈ 11.876. Therefore, the base of the parallelogram is approximately 11.876 units.

Answer 2

Area of the parallelogram:
A = a * h
where a is the base and h is the height;
91 = a * h
a = 2 h + 1
( 2 h + 1 ) * h = 91
2 h² + h - 91 = 0
h 1/2 = ( - 1 +/- √(1+728)) / 4 = ( - 1 +/- 27) / 4
h = 6.5 ( another solution is negative )
a = 2 * 6.5 + 1 = 13 + 1 = 14
Answer:
The base is 14 units and the height 6.5 units long.