Defence Exam > Defence Questions > The sides of a right angled triangle are equa...
Start Learning for Free
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?
- a)6 cm²
- b)8 cm²
- c)10 cm²
- d)12 cm²
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The sides of a right angled triangle are equal to three consecutive nu...
Most Upvoted Answer
The sides of a right angled triangle are equal to three consecutive nu...
To solve this problem, let's assume that the three consecutive numbers are x, x+1, and x+2.
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. In this case, we have:
x^2 + (x+1)^2 = (x+2)^2
Expanding and simplifying this equation, we get:
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
Combining like terms, we have:
2x^2 + 2x + 1 = x^2 + 4x + 4
Subtracting x^2 and 4x from both sides, we get:
x^2 - 2x - 3 = 0
Factoring this quadratic equation, we get:
(x - 3)(x + 1) = 0
So, x = 3 or x = -1. Since we are dealing with lengths, we can ignore the negative solution. Therefore, x = 3.
Thus, the sides of the right-angled triangle are 3 cm, 4 cm, and 5 cm.
The area of a right-angled triangle is given by the formula: Area = (1/2) * base * height.
In this case, the base and height of the right-angled triangle are 3 cm and 4 cm, respectively.
Therefore, the area of the right-angled triangle is:
Area = (1/2) * 3 cm * 4 cm = 6 cm^2
So, the area of such a triangle can be 6 cm^2, which corresponds to option (a).
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. In this case, we have:
x^2 + (x+1)^2 = (x+2)^2
Expanding and simplifying this equation, we get:
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
Combining like terms, we have:
2x^2 + 2x + 1 = x^2 + 4x + 4
Subtracting x^2 and 4x from both sides, we get:
x^2 - 2x - 3 = 0
Factoring this quadratic equation, we get:
(x - 3)(x + 1) = 0
So, x = 3 or x = -1. Since we are dealing with lengths, we can ignore the negative solution. Therefore, x = 3.
Thus, the sides of the right-angled triangle are 3 cm, 4 cm, and 5 cm.
The area of a right-angled triangle is given by the formula: Area = (1/2) * base * height.
In this case, the base and height of the right-angled triangle are 3 cm and 4 cm, respectively.
Therefore, the area of the right-angled triangle is:
Area = (1/2) * 3 cm * 4 cm = 6 cm^2
So, the area of such a triangle can be 6 cm^2, which corresponds to option (a).
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer?
Question Description
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer?.
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer?.
Solutions for The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ?a)6 cm²b)8 cm²c)10 cm²d)12 cm²Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup