Class 8 Exam > Class 8 Questions > Consider a square ABCD of side length 16. Let...
Start Learning for Free
Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is?
Most Upvoted Answer
Consider a square ABCD of side length 16. Let E, F be points on CD suc...
Understanding the Problem
We have a square ABCD with side length 16. Points E and F are positioned on side CD such that CE = EF = FD. Since CD is 16 units long, each segment will measure:
Positioning the Points
Let's locate the points in a coordinate system:
Finding the Equations of Lines
To find point M where lines AE and BF intersect, we need to derive the equations of these lines:
1. Line AE:
- Slope = (5.33 - 16) / (16 - 0) = -10.67 / 16
- Equation: y - 16 = (-10.67/16)(x - 0)
2. Line BF:
- Slope = (10.67 - 16) / (16 - 16) (vertical line)
- Equation: x = 16
Finding Intersecting Point M
Now we substitute x = 16 in the equation of line AE to find M's coordinates:
Calculating Area of Triangle MAB
The area of triangle MAB can be calculated using the formula:
Thus, the area is:
Conclusion
The area of triangle MAB is approximately 85.36 square units.
We have a square ABCD with side length 16. Points E and F are positioned on side CD such that CE = EF = FD. Since CD is 16 units long, each segment will measure:
- CE = EF = FD = 16/3 = 5.33 (approximately)
Positioning the Points
Let's locate the points in a coordinate system:
- A(0, 16)
- B(16, 16)
- C(16, 0)
- D(0, 0)
- E(16, 5.33)
- F(16, 10.67)
Finding the Equations of Lines
To find point M where lines AE and BF intersect, we need to derive the equations of these lines:
1. Line AE:
- Slope = (5.33 - 16) / (16 - 0) = -10.67 / 16
- Equation: y - 16 = (-10.67/16)(x - 0)
2. Line BF:
- Slope = (10.67 - 16) / (16 - 16) (vertical line)
- Equation: x = 16
Finding Intersecting Point M
Now we substitute x = 16 in the equation of line AE to find M's coordinates:
- y = (-10.67/16)(16) + 16
- y = 5.33
- M(16, 5.33)
Calculating Area of Triangle MAB
The area of triangle MAB can be calculated using the formula:
- Area = 0.5 * base * height
- Base AB = 16 units
- Height = 16 - 5.33 = 10.67 units
Thus, the area is:
- Area = 0.5 * 16 * 10.67 = 85.36 square units (approximately)
Conclusion
The area of triangle MAB is approximately 85.36 square units.
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
Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is?
Question Description
Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? 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 Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is?.
Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? 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 Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is?.
Solutions for Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? 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 Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is?, a detailed solution for Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? has been provided alongside types of Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? theory, EduRev gives you an
ample number of questions to practice Consider a square ABCD of side length 16. Let E, F be points on CD such that CE=EF=FD. Let the line BF and AE meet in M. The area of triangle MAB is? 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