Class 9 Exam > Class 9 Questions > The sides of a triangle are in the ratio of 5...
Start Learning for Free
The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?
- a)32 cm2
- b)120 cm²
- c)67 cm2
- d)72cm2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The sides of a triangle are in the ratio of 5: 12: 13. If its perimete...
Given that the sides of the triangle are in the ratio 5:12:13 and the perimeter is 60 cm, we can follow these steps:
- Find the actual side lengths: Let the common ratio factor be xxx.
So, the sides of the triangle are 5x, 12x, and 13x.The perimeter is the sum of the sides:5x+12x+13x=60
30x=60
x=2
- Therefore, the sides of the triangle are:5x=10 cm,12x=24 cm,13x=26 cm.
- Check if it's a right-angled triangle: The sides are in the ratio 5:12:13, which is a well-known Pythagorean triplet, meaning it is a right-angled triangle.
- Find the area: For a right-angled triangle, the area is:Area=12×Base×HeightHere, the base is 10 cm, and the height is 24 cm:Area=12×10×24=120 cm^2
Thus, the correct answer is:
1. 120 cm².
Most Upvoted Answer
The sides of a triangle are in the ratio of 5: 12: 13. If its perimete...
Free Test
FREE
| Start Free Test |
Community Answer
The sides of a triangle are in the ratio of 5: 12: 13. If its perimete...
Understanding the Triangle's Sides
Given the sides of the triangle in the ratio of 5:12:13, we can denote the sides as:
- Side 1 = 5x
- Side 2 = 12x
- Side 3 = 13x
The perimeter of the triangle is given as 60 cm. Thus, we have:
Calculating the Value of x
\[
\text{Perimeter} = 5x + 12x + 13x = 30x
\]
Setting this equal to the given perimeter:
\[
30x = 60 \implies x = 2
\]
Finding the Lengths of the Sides
Now we can find the lengths of each side:
- Side 1 = \(5 \times 2 = 10 \, \text{cm}\)
- Side 2 = \(12 \times 2 = 24 \, \text{cm}\)
- Side 3 = \(13 \times 2 = 26 \, \text{cm}\)
Verifying the Type of Triangle
Since the sides are in the ratio 5:12:13, we can confirm that this is a right triangle because:
\[
10^2 + 24^2 = 100 + 576 = 676 = 26^2
\]
Calculating the Area of the Triangle
For a right triangle, the area can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Taking the two shorter sides as base and height:
\[
\text{Area} = \frac{1}{2} \times 10 \times 24 = \frac{240}{2} = 120 \, \text{cm}^2
\]
Conclusion
Thus, the area of the triangle is \(120 \, \text{cm}^2\), confirming that the correct answer is option 'B'.
Given the sides of the triangle in the ratio of 5:12:13, we can denote the sides as:
- Side 1 = 5x
- Side 2 = 12x
- Side 3 = 13x
The perimeter of the triangle is given as 60 cm. Thus, we have:
Calculating the Value of x
\[
\text{Perimeter} = 5x + 12x + 13x = 30x
\]
Setting this equal to the given perimeter:
\[
30x = 60 \implies x = 2
\]
Finding the Lengths of the Sides
Now we can find the lengths of each side:
- Side 1 = \(5 \times 2 = 10 \, \text{cm}\)
- Side 2 = \(12 \times 2 = 24 \, \text{cm}\)
- Side 3 = \(13 \times 2 = 26 \, \text{cm}\)
Verifying the Type of Triangle
Since the sides are in the ratio 5:12:13, we can confirm that this is a right triangle because:
\[
10^2 + 24^2 = 100 + 576 = 676 = 26^2
\]
Calculating the Area of the Triangle
For a right triangle, the area can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Taking the two shorter sides as base and height:
\[
\text{Area} = \frac{1}{2} \times 10 \times 24 = \frac{240}{2} = 120 \, \text{cm}^2
\]
Conclusion
Thus, the area of the triangle is \(120 \, \text{cm}^2\), confirming that the correct answer is option 'B'.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
Question Description
The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer?.
The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sides of a triangle are in the ratio of 5: 12: 13. If its perimeter is 60 cm, then what is its area?a)32 cm2b)120 cm²c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup