Class 10 Exam > Class 10 Questions > The difference between altitude and base of a...
Start Learning for Free
The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?
- a)24 cm
- b)31 cm
- c)34 cm
- d)can't be determined
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The difference between altitude and base of a right angled triangle is...
Free Test
FREE
| Start Free Test |
Community Answer
The difference between altitude and base of a right angled triangle is...
Given: Altitude - Base = 17 cm, Hypotenuse = 25 cm
Let's assume the base of the right angled triangle to be 'b' and altitude to be 'h'.
Using Pythagoras theorem, we know that:
Hypotenuse^2 = Base^2 + Altitude^2
25^2 = b^2 + h^2
625 = b^2 + h^2 ----(1)
We are also given that Altitude - Base = 17 cm i.e h - b = 17 or h = b + 17 ----(2)
Substituting equation (2) in (1), we get:
625 = b^2 + (b+17)^2
625 = b^2 + b^2 + 34b + 289
2b^2 + 34b - 336 = 0
b^2 + 17b - 168 = 0
(b+24)(b-7) = 0
Hence, b = 7 (as the base cannot be negative)
Using equation (2), h = 7 + 17 = 24
Therefore, the sum of base and altitude of this triangle is:
b + h = 7 + 24 = 31 cm
Hence, option (b) is the correct answer.
Let's assume the base of the right angled triangle to be 'b' and altitude to be 'h'.
Using Pythagoras theorem, we know that:
Hypotenuse^2 = Base^2 + Altitude^2
25^2 = b^2 + h^2
625 = b^2 + h^2 ----(1)
We are also given that Altitude - Base = 17 cm i.e h - b = 17 or h = b + 17 ----(2)
Substituting equation (2) in (1), we get:
625 = b^2 + (b+17)^2
625 = b^2 + b^2 + 34b + 289
2b^2 + 34b - 336 = 0
b^2 + 17b - 168 = 0
(b+24)(b-7) = 0
Hence, b = 7 (as the base cannot be negative)
Using equation (2), h = 7 + 17 = 24
Therefore, the sum of base and altitude of this triangle is:
b + h = 7 + 24 = 31 cm
Hence, option (b) is the correct answer.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer?
Question Description
The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer?.
The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle is ?a)24 cmb)31 cmc)34 cmd)can't be determinedCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
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