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Answer :
To find the length of the base of the triangle given its area and height, we can use the formula for the area of a triangle:
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
We are given:
- The area [tex]\( A = 38.4 \, \text{cm}^2 \)[/tex]
- The height of the triangle [tex]\( h = 12.8 \, \text{cm} \)[/tex]
We need to find the base of the triangle. To do this, we can rearrange the formula to solve for the base:
1. Start with the formula for the area of a triangle:
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ 38.4 = \frac{1}{2} \times \text{base} \times 12.8 \][/tex]
3. To isolate the base, first remove the fraction by multiplying both sides by 2:
[tex]\[ 2 \times 38.4 = \text{base} \times 12.8 \][/tex]
[tex]\[ 76.8 = \text{base} \times 12.8 \][/tex]
4. Finally, divide both sides by 12.8 to solve for the base:
[tex]\[ \text{base} = \frac{76.8}{12.8} \][/tex]
5. Simplify the division:
[tex]\[ \text{base} = 6 \][/tex]
Therefore, the length of the base of the triangle is 6 centimeters.
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
We are given:
- The area [tex]\( A = 38.4 \, \text{cm}^2 \)[/tex]
- The height of the triangle [tex]\( h = 12.8 \, \text{cm} \)[/tex]
We need to find the base of the triangle. To do this, we can rearrange the formula to solve for the base:
1. Start with the formula for the area of a triangle:
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ 38.4 = \frac{1}{2} \times \text{base} \times 12.8 \][/tex]
3. To isolate the base, first remove the fraction by multiplying both sides by 2:
[tex]\[ 2 \times 38.4 = \text{base} \times 12.8 \][/tex]
[tex]\[ 76.8 = \text{base} \times 12.8 \][/tex]
4. Finally, divide both sides by 12.8 to solve for the base:
[tex]\[ \text{base} = \frac{76.8}{12.8} \][/tex]
5. Simplify the division:
[tex]\[ \text{base} = 6 \][/tex]
Therefore, the length of the base of the triangle is 6 centimeters.
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