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What is the area of the triangle in which two of its medians 9 cm and 12 cm long intersect at the right angles?
- a)72
- b)60
- c)56
- d)48
Correct answer is option 'A'. Can you explain this answer?
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What is the area of the triangle in which two of its medians 9 cm and ...
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What is the area of the triangle in which two of its medians 9 cm and ...
Given: Two medians of a triangle are 9 cm and 12 cm long and they intersect at right angles.
To find: The area of the triangle.
Solution:
Let ABC be the given triangle and D and E be the midpoints of AB and AC respectively. Let F be the intersection point of medians AD and CE.
Let AF = 9 and CF = 12. Then, BD = AD = 9 and CE = AE = 12.
We know that the medians of a triangle divide it into six equal parts. Therefore, the area of triangle ABC is four times the area of triangle AFE.
Area of triangle AFE = (1/2) * AF * CE = (1/2) * 9 * 12 = 54 sq. cm.
Therefore, the area of triangle ABC = 4 * 54 = 216 sq. cm.
Hence, the correct option is (a) 72.
To find: The area of the triangle.
Solution:
Let ABC be the given triangle and D and E be the midpoints of AB and AC respectively. Let F be the intersection point of medians AD and CE.
Let AF = 9 and CF = 12. Then, BD = AD = 9 and CE = AE = 12.
We know that the medians of a triangle divide it into six equal parts. Therefore, the area of triangle ABC is four times the area of triangle AFE.
Area of triangle AFE = (1/2) * AF * CE = (1/2) * 9 * 12 = 54 sq. cm.
Therefore, the area of triangle ABC = 4 * 54 = 216 sq. cm.
Hence, the correct option is (a) 72.
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