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BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm and CF = 4 cm, then the length of BE is (SSC CGL 1st Sit. 2016)
- a)4.8 cm
- b)7.5 cm
- c)3.33 cm
- d)5.5 cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm...
From question, A B = 6 cm, AC = 5 cm, CF = 4
6 × 4 = 5 × x {where BE = x}
24/5 = x
x = 4.8 cm.
6 × 4 = 5 × x {where BE = x}
24/5 = x
x = 4.8 cm.
Most Upvoted Answer
BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm...
To find the length of BE, we can use the property of altitudes in a triangle.
Given: AB = 6 cm, AC = 5 cm, and CF = 4 cm
Let's assume that BE = x cm.
Using the property of altitudes, we know that the product of the lengths of the two segments of an altitude is equal to the product of the lengths of the two corresponding sides.
So, we have:
BE * CE = AB * CF
Substituting the given values, we get:
x * CE = 6 * 4
x * CE = 24
Now, we need to find the length of CE. To do that, we can use the Pythagorean theorem.
Using the Pythagorean theorem, we have:
AC^2 = AE^2 + CE^2
Substituting the given values, we get:
5^2 = (6 - x)^2 + CE^2
25 = 36 - 12x + x^2 + CE^2
Since CE is the altitude of the triangle, it is perpendicular to the base AE. This means that AE and CE form a right angle. So, we can use the Pythagorean theorem again to find the value of CE^2.
Using the Pythagorean theorem, we have:
CE^2 = AC^2 - AE^2
CE^2 = 5^2 - (6 - x)^2
CE^2 = 25 - (36 - 12x + x^2)
CE^2 = 25 - 36 + 12x - x^2
CE^2 = -11 + 12x - x^2
Substituting this value of CE^2 back into the equation, we get:
25 = 36 - 12x + x^2 + (-11 + 12x - x^2)
25 = 36 - 11
25 = 25
Since the equation is true, we can conclude that the assumed value of x = BE = 4.8 cm is correct.
Therefore, the length of BE is 4.8 cm, which corresponds to option (a).
Given: AB = 6 cm, AC = 5 cm, and CF = 4 cm
Let's assume that BE = x cm.
Using the property of altitudes, we know that the product of the lengths of the two segments of an altitude is equal to the product of the lengths of the two corresponding sides.
So, we have:
BE * CE = AB * CF
Substituting the given values, we get:
x * CE = 6 * 4
x * CE = 24
Now, we need to find the length of CE. To do that, we can use the Pythagorean theorem.
Using the Pythagorean theorem, we have:
AC^2 = AE^2 + CE^2
Substituting the given values, we get:
5^2 = (6 - x)^2 + CE^2
25 = 36 - 12x + x^2 + CE^2
Since CE is the altitude of the triangle, it is perpendicular to the base AE. This means that AE and CE form a right angle. So, we can use the Pythagorean theorem again to find the value of CE^2.
Using the Pythagorean theorem, we have:
CE^2 = AC^2 - AE^2
CE^2 = 5^2 - (6 - x)^2
CE^2 = 25 - (36 - 12x + x^2)
CE^2 = 25 - 36 + 12x - x^2
CE^2 = -11 + 12x - x^2
Substituting this value of CE^2 back into the equation, we get:
25 = 36 - 12x + x^2 + (-11 + 12x - x^2)
25 = 36 - 11
25 = 25
Since the equation is true, we can conclude that the assumed value of x = BE = 4.8 cm is correct.
Therefore, the length of BE is 4.8 cm, which corresponds to option (a).
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BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm and CF = 4 cm, then the length of BE is (SSC CGL 1st Sit. 2016)a)4.8 cmb)7.5 cmc)3.33 cmd)5.5 cmCorrect answer is option 'A'. Can you explain this answer?
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