Class 8 Exam > Class 8 Questions > ABCD is a parallelogram whose diagonals inter...
Start Learning for Free
ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals.
Most Upvoted Answer
ABCD is a parallelogram whose diagonals intersect each other at right ...
Understanding the Parallelogram ABCD
In the parallelogram ABCD, the diagonals AC and BD intersect at point O. Given that the diagonals bisect each other at right angles, we can utilize the properties of right triangles to find the lengths of the sides.
Length of the Diagonals
- Diagonal AC = 6 cm
- Diagonal BD = 8 cm
Since the diagonals bisect each other, we can determine the half lengths:
- AO = CO = AC / 2 = 6 cm / 2 = 3 cm
- BO = DO = BD / 2 = 8 cm / 2 = 4 cm
Applying the Pythagorean Theorem
To find the lengths of the sides AB and AD, we use the Pythagorean theorem in triangle AOB:
- AB^2 = AO^2 + BO^2
- AB^2 = (3 cm)^2 + (4 cm)^2
- AB^2 = 9 cm^2 + 16 cm^2
- AB^2 = 25 cm^2
- AB = √25 cm^2 = 5 cm
Since the opposite sides of a parallelogram are equal, we have:
- AD = AB = 5 cm
Conclusion
Thus, the lengths of all sides of the parallelogram ABCD are:
- AB = 5 cm
- BC = 5 cm
- CD = 5 cm
- DA = 5 cm
In summary, in parallelogram ABCD with diagonals intersecting at right angles, all sides measure 5 cm.
In the parallelogram ABCD, the diagonals AC and BD intersect at point O. Given that the diagonals bisect each other at right angles, we can utilize the properties of right triangles to find the lengths of the sides.
Length of the Diagonals
- Diagonal AC = 6 cm
- Diagonal BD = 8 cm
Since the diagonals bisect each other, we can determine the half lengths:
- AO = CO = AC / 2 = 6 cm / 2 = 3 cm
- BO = DO = BD / 2 = 8 cm / 2 = 4 cm
Applying the Pythagorean Theorem
To find the lengths of the sides AB and AD, we use the Pythagorean theorem in triangle AOB:
- AB^2 = AO^2 + BO^2
- AB^2 = (3 cm)^2 + (4 cm)^2
- AB^2 = 9 cm^2 + 16 cm^2
- AB^2 = 25 cm^2
- AB = √25 cm^2 = 5 cm
Since the opposite sides of a parallelogram are equal, we have:
- AD = AB = 5 cm
Conclusion
Thus, the lengths of all sides of the parallelogram ABCD are:
- AB = 5 cm
- BC = 5 cm
- CD = 5 cm
- DA = 5 cm
In summary, in parallelogram ABCD with diagonals intersecting at right angles, all sides measure 5 cm.
Community Answer
ABCD is a parallelogram whose diagonals intersect each other at right ...
you can use the parallelogram formula
Attention Class 8 Students!
To make sure you are not studying endlessly, EduRev has designed Class 8 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 8.
|
Explore Courses for Class 8 exam
|
|
Similar Class 8 Doubts
Top Courses for Class 8View all
ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals.
Question Description
ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals..
ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals..
Solutions for ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. in English & in Hindi are available as part of our courses for Class 8.
Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
Here you can find the meaning of ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. defined & explained in the simplest way possible. Besides giving the explanation of
ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals., a detailed solution for ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. has been provided alongside types of ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. theory, EduRev gives you an
ample number of questions to practice ABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of the diagonals is 6cm and 8 cm, find the lengths of all sides of the diagonals. tests, examples and also practice Class 8 tests.
|
|
Explore Courses for Class 8 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
|
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