Answer :
Certainly! To find the correct dimensions of a parallelogram that has an area of 20 square inches, we use the fundamental formula for the area of a parallelogram:
[tex]\[ \text{Area} = \text{base} \times \text{height} \][/tex]
We are given the area as 20 square inches and asked to match this to one of the provided pairs of base ([tex]\(x\)[/tex]) and height ([tex]\(h\)[/tex]). Here are the given options:
A. [tex]\(x = 3.06\)[/tex] in, [tex]\(h = 6.54\)[/tex] in
B. [tex]\(x = 6.22\)[/tex] in, [tex]\(h = 3.23\)[/tex] in
C. [tex]\(x = 4.00\)[/tex] in, [tex]\(h = 5.00\)[/tex] in
D. [tex]\(x = 7.78\)[/tex] in, [tex]\(h = 2.57\)[/tex] in
We will check each pair to find which pair satisfies the area condition.
### Option A: [tex]\(x = 3.06\)[/tex] in, [tex]\(h = 6.54\)[/tex] in
[tex]\[ \text{Area} = 3.06 \times 6.54 \approx 20.00 \text{ square inches} \][/tex]
### Option B: [tex]\(x = 6.22\)[/tex] in, [tex]\(h = 3.23\)[/tex] in
[tex]\[ \text{Area} = 6.22 \times 3.23 \approx 20.08 \text{ square inches} \][/tex]
### Option C: [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 D: [tex]\(x = 7.78\)[/tex] in, [tex]\(h = 2.57\)[/tex] in
[tex]\[ \text{Area} = 7.78 \times 2.57 \approx 20.00 \text{ square inches} \][/tex]
Therefore, after checking each pair of base and height, we find that the pair that exactly matches the area of 20 square inches is:
[tex]\[ \boxed{4.00 \text{ in, } 5.00 \text{ in}} \][/tex]
So, the dimensions of the parallelogram are [tex]\(x = 4.00\)[/tex] inches and [tex]\(h = 5.00\)[/tex] inches, which is Option C.
[tex]\[ \text{Area} = \text{base} \times \text{height} \][/tex]
We are given the area as 20 square inches and asked to match this to one of the provided pairs of base ([tex]\(x\)[/tex]) and height ([tex]\(h\)[/tex]). Here are the given options:
A. [tex]\(x = 3.06\)[/tex] in, [tex]\(h = 6.54\)[/tex] in
B. [tex]\(x = 6.22\)[/tex] in, [tex]\(h = 3.23\)[/tex] in
C. [tex]\(x = 4.00\)[/tex] in, [tex]\(h = 5.00\)[/tex] in
D. [tex]\(x = 7.78\)[/tex] in, [tex]\(h = 2.57\)[/tex] in
We will check each pair to find which pair satisfies the area condition.
### Option A: [tex]\(x = 3.06\)[/tex] in, [tex]\(h = 6.54\)[/tex] in
[tex]\[ \text{Area} = 3.06 \times 6.54 \approx 20.00 \text{ square inches} \][/tex]
### Option B: [tex]\(x = 6.22\)[/tex] in, [tex]\(h = 3.23\)[/tex] in
[tex]\[ \text{Area} = 6.22 \times 3.23 \approx 20.08 \text{ square inches} \][/tex]
### Option C: [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 D: [tex]\(x = 7.78\)[/tex] in, [tex]\(h = 2.57\)[/tex] in
[tex]\[ \text{Area} = 7.78 \times 2.57 \approx 20.00 \text{ square inches} \][/tex]
Therefore, after checking each pair of base and height, we find that the pair that exactly matches the area of 20 square inches is:
[tex]\[ \boxed{4.00 \text{ in, } 5.00 \text{ in}} \][/tex]
So, the dimensions of the parallelogram are [tex]\(x = 4.00\)[/tex] inches and [tex]\(h = 5.00\)[/tex] inches, which is Option C.
