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Answer :
Sure, let's solve these two questions step by step.
### Question 17
We need to find the height of a trapezoid with the following dimensions:
- Base1 ([tex]\(b_1\)[/tex]) = 19.5 cm
- Base2 ([tex]\(b_2\)[/tex]) = 24.5 cm
- Area ([tex]\(A\)[/tex]) = 154 square cm
We will use the formula for the area of a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times \text{height} \][/tex]
Re-arranging this formula to solve for the height ([tex]\(h\)[/tex]), we get:
[tex]\[ \text{height} = \frac{2 \times \text{Area}}{b_1 + b_2} \][/tex]
Substituting the given values into the formula, we have:
[tex]\[ \text{height} = \frac{2 \times 154}{19.5 + 24.5} \][/tex]
Calculating the denominator:
[tex]\[ 19.5 + 24.5 = 44 \][/tex]
So:
[tex]\[ \text{height} = \frac{2 \times 154}{44} \][/tex]
[tex]\[ \text{height} = \frac{308}{44} \][/tex]
[tex]\[ \text{height} = 7.0 \][/tex]
Therefore, the height of the trapezoid is 7.0 cm.
### Question 18
We need to find the length of the other base of a trapezoid with the following dimensions:
- Height ([tex]\(h\)[/tex]) = 40 inches
- Base1 ([tex]\(b_1\)[/tex]) = 15 inches
- Area ([tex]\(A\)[/tex]) = 2400 square inches
Again, using the area formula for a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times \text{height} \][/tex]
Re-arranging this formula to solve for the other base ([tex]\(b_2\)[/tex]), we get:
[tex]\[ b_2 = \frac{2 \times \text{Area}}{\text{height}} - b_1 \][/tex]
Substituting the given values into the formula, we have:
[tex]\[ b_2 = \frac{2 \times 2400}{40} - 15 \][/tex]
Calculating the numerator for the first term:
[tex]\[ 2 \times 2400 = 4800 \][/tex]
So:
[tex]\[ b_2 = \frac{4800}{40} - 15 \][/tex]
[tex]\[ b_2 = 120 - 15 \][/tex]
[tex]\[ b_2 = 105.0 \][/tex]
Therefore, the length of the other base of the trapezoid is 105.0 inches.
### Question 17
We need to find the height of a trapezoid with the following dimensions:
- Base1 ([tex]\(b_1\)[/tex]) = 19.5 cm
- Base2 ([tex]\(b_2\)[/tex]) = 24.5 cm
- Area ([tex]\(A\)[/tex]) = 154 square cm
We will use the formula for the area of a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times \text{height} \][/tex]
Re-arranging this formula to solve for the height ([tex]\(h\)[/tex]), we get:
[tex]\[ \text{height} = \frac{2 \times \text{Area}}{b_1 + b_2} \][/tex]
Substituting the given values into the formula, we have:
[tex]\[ \text{height} = \frac{2 \times 154}{19.5 + 24.5} \][/tex]
Calculating the denominator:
[tex]\[ 19.5 + 24.5 = 44 \][/tex]
So:
[tex]\[ \text{height} = \frac{2 \times 154}{44} \][/tex]
[tex]\[ \text{height} = \frac{308}{44} \][/tex]
[tex]\[ \text{height} = 7.0 \][/tex]
Therefore, the height of the trapezoid is 7.0 cm.
### Question 18
We need to find the length of the other base of a trapezoid with the following dimensions:
- Height ([tex]\(h\)[/tex]) = 40 inches
- Base1 ([tex]\(b_1\)[/tex]) = 15 inches
- Area ([tex]\(A\)[/tex]) = 2400 square inches
Again, using the area formula for a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times \text{height} \][/tex]
Re-arranging this formula to solve for the other base ([tex]\(b_2\)[/tex]), we get:
[tex]\[ b_2 = \frac{2 \times \text{Area}}{\text{height}} - b_1 \][/tex]
Substituting the given values into the formula, we have:
[tex]\[ b_2 = \frac{2 \times 2400}{40} - 15 \][/tex]
Calculating the numerator for the first term:
[tex]\[ 2 \times 2400 = 4800 \][/tex]
So:
[tex]\[ b_2 = \frac{4800}{40} - 15 \][/tex]
[tex]\[ b_2 = 120 - 15 \][/tex]
[tex]\[ b_2 = 105.0 \][/tex]
Therefore, the length of the other base of the trapezoid is 105.0 inches.
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