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The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?

Hint: Use the formula that uses trigonometry to find the area of any non-right triangle in order to solve this problem.

[tex]\[ A_{\text {triangle }} = \frac{1}{2} a b \sin (C) \][/tex]

A. [tex]\( x = 3.06 \, \text{in}, \, h = 6.54 \, \text{in} \)[/tex]

B. [tex]\( x = 4.00 \, \text{in}, \, h = 5.00 \, \text{in} \)[/tex]

C. [tex]\( x = 7.78 \, \text{in}, \, h = 2.57 \, \text{in} \)[/tex]

D. [tex]\( x = 6.22 \, \text{in}, \, h = 3.23 \, \text{in} \)[/tex]



Answer :

GinnyAnswer
To determine the dimensions of the parallelogram that has an area of 20 square inches, let us examine each option and calculate the respective areas to find the one that fits the description. Given the potential values for [tex]\( x \)[/tex] and [tex]\( h \)[/tex] (where [tex]\( x \)[/tex] is typically the base and [tex]\( h \)[/tex] the height).

We will use the formula for the area of a parallelogram:
[tex]\[ \text{Area} = \text{Base} \times \text{Height} \][/tex]

### Option A: [tex]\( x = 3.06 \)[/tex] in, [tex]\( h = 6.54 \)[/tex] in
[tex]\[ \text{Area} = 3.06 \times 6.54 = 20.01 \text{ square inches} \][/tex]

### Option B: [tex]\( x = 4.00 \)[/tex] in, [tex]\( h = 5.00 \)[/tex] in
[tex]\[ \text{Area} = 4.00 \times 5.00 = 20.00 \text{ square inches} \][/tex]

### Option C: [tex]\( x = 7.78 \)[/tex] in, [tex]\( h = 2.57 \)[/tex] in
[tex]\[ \text{Area} = 7.78 \times 2.57 = 19.99 \text{ square inches} \][/tex]

### Option D: [tex]\( x = 6.22 \)[/tex] in, [tex]\( h = 3.23 \)[/tex] in
[tex]\[ \text{Area} = 6.22 \times 3.23 = 20.09 \text{ square inches} \][/tex]

Now, let us compare the calculated areas with the given area of the parallelogram, which is 20 square inches.

- Option A gives an area of 20.01 square inches.
- Option B gives an area of 20.00 square inches.
- Option C gives an area of 19.99 square inches.
- Option D gives an area of 20.09 square inches.

Among these options, only Option B gives an area exactly equal to 20.00 square inches.

Therefore, the correct answer is:

Option B: [tex]\( x = 4.00 \)[/tex] in, [tex]\( h = 5.00 \)[/tex] in.

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