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The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side is
- a)22.4 cm
- b)67.2 cm
- c)44.8 cm
- d)60 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The sides of a triangle are in the ratio 13:14:15 and its perimeter is...
Ratio of sides = 13 : 14 : 15
Perimeter of triangle = 168 cm
Let the sides are 13x, 14x, and 15x
∴ 13x + 14x + 15x = 168
⇒ 42x = 168
⇒ x = 4
∴ sides are 13 x 4 = 52 cm
14 x 4 = 56 cm
15 x 4 = 60 cm
s = sum of sides/2 = 168/2 = 84
∴ Area of the triangle
Perimeter of triangle = 168 cm
Let the sides are 13x, 14x, and 15x
∴ 13x + 14x + 15x = 168
⇒ 42x = 168
⇒ x = 4
∴ sides are 13 x 4 = 52 cm
14 x 4 = 56 cm
15 x 4 = 60 cm
s = sum of sides/2 = 168/2 = 84
∴ Area of the triangle
Let BL be altitude on the largest side AC of A ABC
Area of Δ ABC = 1344 cm2
⇒ 1/2 x base x altitude = 1344 cm2
⇒ 1/2 x AC x BL = 1344 cm2
⇒ 30 BL = 1344
⇒ BL = 1344/30 = 44.8 cm
Most Upvoted Answer
The sides of a triangle are in the ratio 13:14:15 and its perimeter is...
Given:
The sides of a triangle are in the ratio 13:14:15.
The perimeter of the triangle is 168 cm.
To find:
The length of the altitude corresponding to the longest side.
Solution:
Let's assume the sides of the triangle are 13x, 14x, and 15x, where x is a common factor.
Step 1: Finding the value of x
The perimeter of a triangle is the sum of its three sides.
So, we have: 13x + 14x + 15x = 168
42x = 168
Dividing both sides by 42, we get:
x = 4
Therefore, the sides of the triangle are 52 cm, 56 cm, and 60 cm.
Step 2: Finding the length of the altitude corresponding to the longest side
In a triangle, the altitude corresponding to the longest side divides the triangle into two right triangles.
Let's consider the triangle with sides 52 cm, 56 cm, and 60 cm.
The longest side is 60 cm.
Using the Pythagorean theorem:
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume the altitude corresponding to the longest side is h.
By applying the Pythagorean theorem, we have:
(52)^2 = h^2 + (56 - h)^2
Simplifying the equation, we get:
2704 = h^2 + 3136 - 112h + h^2
Combining like terms, we have:
2h^2 - 112h + 432 = 0
Solving this quadratic equation, we get:
h = 44.8 or h = 48
Since the altitude of a triangle cannot be greater than the length of the corresponding side, we can eliminate the option h = 48.
Therefore, the length of the altitude corresponding to the longest side is 44.8 cm.
Hence, the correct answer is option c) 44.8 cm.
The sides of a triangle are in the ratio 13:14:15.
The perimeter of the triangle is 168 cm.
To find:
The length of the altitude corresponding to the longest side.
Solution:
Let's assume the sides of the triangle are 13x, 14x, and 15x, where x is a common factor.
Step 1: Finding the value of x
The perimeter of a triangle is the sum of its three sides.
So, we have: 13x + 14x + 15x = 168
42x = 168
Dividing both sides by 42, we get:
x = 4
Therefore, the sides of the triangle are 52 cm, 56 cm, and 60 cm.
Step 2: Finding the length of the altitude corresponding to the longest side
In a triangle, the altitude corresponding to the longest side divides the triangle into two right triangles.
Let's consider the triangle with sides 52 cm, 56 cm, and 60 cm.
The longest side is 60 cm.
Using the Pythagorean theorem:
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume the altitude corresponding to the longest side is h.
By applying the Pythagorean theorem, we have:
(52)^2 = h^2 + (56 - h)^2
Simplifying the equation, we get:
2704 = h^2 + 3136 - 112h + h^2
Combining like terms, we have:
2h^2 - 112h + 432 = 0
Solving this quadratic equation, we get:
h = 44.8 or h = 48
Since the altitude of a triangle cannot be greater than the length of the corresponding side, we can eliminate the option h = 48.
Therefore, the length of the altitude corresponding to the longest side is 44.8 cm.
Hence, the correct answer is option c) 44.8 cm.
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The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side isa)22.4 cmb)67.2 cmc)44.8 cmd)60 cmCorrect answer is option 'C'. Can you explain this answer?
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The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side isa)22.4 cmb)67.2 cmc)44.8 cmd)60 cmCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side isa)22.4 cmb)67.2 cmc)44.8 cmd)60 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side isa)22.4 cmb)67.2 cmc)44.8 cmd)60 cmCorrect answer is option 'C'. Can you explain this answer?.
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