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The ratio of the sides of Δ ABC is 1:2:4. What is the ratio of the altitudes drawn onto these sides?
- a)4:2:1
- b)1:2:4
- c)1:4:16
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of the sides of Δ ABC is 1:2:4. What is the ratio of th...
Sum of any two sides should be greater than third side.
here 1+2=3 is not less than 4 ,
1+2<4 ,so="" triangle="" is="" not="" possible.="" ,so="" triangle="" is="" not="">
here 1+2=3 is not less than 4 ,
1+2<4 ,so="" triangle="" is="" not="" possible.="" ,so="" triangle="" is="" not="">
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The ratio of the sides of Δ ABC is 1:2:4. What is the ratio of th...
Ratio of the sides of ABC
The given ratio of the sides of triangle ABC is 1:2:4. This means that the lengths of the sides of the triangle are in the ratio 1:2:4.
Ratio of the altitudes
To find the ratio of the altitudes drawn onto the sides of triangle ABC, we need to consider the relationship between the sides and altitudes of a triangle.
The altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side. In triangle ABC, let the altitudes be h1, h2, and h3 drawn onto sides AB, BC, and CA respectively.
The ratio of the altitudes can be determined by considering the relationship between the sides and altitudes of a triangle. According to the triangle altitude theorem, the length of an altitude is directly proportional to the length of the side it is drawn onto.
The ratio of the altitudes can be calculated using the formula:
Ratio of altitudes = (Length of side 1 / Length of side 2) = (Length of side 1 / Length of side 3)
Substituting the given ratio of the sides of triangle ABC (1:2:4), we can calculate the ratio of the altitudes as follows:
Ratio of altitudes = (1 / 2) = (1 / 4) = 1:2:4
Answer
Therefore, the correct answer is option D, none of these. The ratio of the altitudes drawn onto the sides of triangle ABC is 1:2:4.
The given ratio of the sides of triangle ABC is 1:2:4. This means that the lengths of the sides of the triangle are in the ratio 1:2:4.
Ratio of the altitudes
To find the ratio of the altitudes drawn onto the sides of triangle ABC, we need to consider the relationship between the sides and altitudes of a triangle.
The altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side. In triangle ABC, let the altitudes be h1, h2, and h3 drawn onto sides AB, BC, and CA respectively.
The ratio of the altitudes can be determined by considering the relationship between the sides and altitudes of a triangle. According to the triangle altitude theorem, the length of an altitude is directly proportional to the length of the side it is drawn onto.
The ratio of the altitudes can be calculated using the formula:
Ratio of altitudes = (Length of side 1 / Length of side 2) = (Length of side 1 / Length of side 3)
Substituting the given ratio of the sides of triangle ABC (1:2:4), we can calculate the ratio of the altitudes as follows:
Ratio of altitudes = (1 / 2) = (1 / 4) = 1:2:4
Answer
Therefore, the correct answer is option D, none of these. The ratio of the altitudes drawn onto the sides of triangle ABC is 1:2:4.
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The ratio of the sides of Δ ABC is 1:2:4. What is the ratio of the altitudes drawn onto these sides?a)4:2:1b)1:2:4c)1:4:16d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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