To determine the correct dimensions of the parallelogram that has an area of 20 square inches, we will use the formula for the area of a parallelogram [tex]\( A = \text{base} \times \text{height} \)[/tex].
Let's go through each option one by one to check which combination of base and height gives us an area of 20 square inches.
### Option A: [tex]\( x = 3.06 \)[/tex] inches, [tex]\( h = 6.54 \)[/tex] inches
[tex]\[ A = 3.06 \times 6.54 \][/tex]
[tex]\[ A \approx 19.9944 \][/tex]
### Option B: [tex]\( x = 7.78 \)[/tex] inches, [tex]\( h = 2.57 \)[/tex] inches
[tex]\[ A = 7.78 \times 2.57 \][/tex]
[tex]\[ A \approx 19.9946 \][/tex]
### Option C: [tex]\( x = 4.00 \)[/tex] inches, [tex]\( h = 5.00 \)[/tex] inches
[tex]\[ A = 4.00 \times 5.00 \][/tex]
[tex]\[ A = 20.00 \][/tex]
### Option D: [tex]\( x = 6.22 \)[/tex] inches, [tex]\( h = 3.23 \)[/tex] inches
[tex]\[ A = 6.22 \times 3.23 \][/tex]
[tex]\[ A \approx 20.0606 \][/tex]
From our calculations, we see that:
- Option A gives an area approximately equal to 19.9944 square inches.
- Option B gives an area approximately equal to 19.9946 square inches.
- Option C gives an area exactly equal to 20.00 square inches.
- Option D gives an area approximately equal to 20.0606 square inches.
The option that results in exactly 20 square inches is Option C: [tex]\( x = 4.00 \)[/tex] inches, [tex]\( h = 5.00 \)[/tex] inches.
Thus, the correct dimensions of the parallelogram are [tex]\( x = 4.00 \)[/tex] inches and [tex]\( h = 5.00 \)[/tex] inches. The correct answer is Option C.
