UPSC Exam > UPSC Questions > Triangle ABC is isosceles with Ab = AC = 7.5 ...
Start Learning for Free
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?
Most Upvoted Answer
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the hei...
Area of Triangle ABC
To find the area of triangle ABC, we can use the formula for the area of a triangle:
- Area = (1/2) × base × height
In this case:
- Base (BC) = 9 cm
- Height (AD) = 6 cm
Calculating the area:
- Area = (1/2) × 9 cm × 6 cm
- Area = 27 cm²
Thus, the area of triangle ABC is 27 cm².
Height from C to Line AE
To find the height from point C to line AE (denote this height as CE), we can analyze the triangle further.
1. Coordinates Setup:
- Place point A at (0, 6).
- Point B will be at (-4.5, 0) and point C at (4.5, 0) since it is isosceles and symmetrical.
2. Finding Line AE:
- The line AE will be the base (BC) where the coordinates of points B and C are (-4.5, 0) and (4.5, 0) respectively.
3. Using Distance Formula:
- The distance from point C (4.5, 0) to line AE (y = 0) is simply the y-coordinate of point C since line AE lies on y=0.
- Therefore, height CE = 0 - 0 = 0 cm.
The height from point C to line AE is 0 cm, as point C lies directly on line AE.
Summary
- Area of Triangle ABC: 27 cm²
- Height from C to line AE (CE): 0 cm
This analysis helps understand the geometric properties of triangle ABC, reinforcing concepts of area and height in isosceles triangles.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
- Area = (1/2) × base × height
In this case:
- Base (BC) = 9 cm
- Height (AD) = 6 cm
Calculating the area:
- Area = (1/2) × 9 cm × 6 cm
- Area = 27 cm²
Thus, the area of triangle ABC is 27 cm².
Height from C to Line AE
To find the height from point C to line AE (denote this height as CE), we can analyze the triangle further.
1. Coordinates Setup:
- Place point A at (0, 6).
- Point B will be at (-4.5, 0) and point C at (4.5, 0) since it is isosceles and symmetrical.
2. Finding Line AE:
- The line AE will be the base (BC) where the coordinates of points B and C are (-4.5, 0) and (4.5, 0) respectively.
3. Using Distance Formula:
- The distance from point C (4.5, 0) to line AE (y = 0) is simply the y-coordinate of point C since line AE lies on y=0.
- Therefore, height CE = 0 - 0 = 0 cm.
The height from point C to line AE is 0 cm, as point C lies directly on line AE.
Summary
- Area of Triangle ABC: 27 cm²
- Height from C to line AE (CE): 0 cm
This analysis helps understand the geometric properties of triangle ABC, reinforcing concepts of area and height in isosceles triangles.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?
Question Description
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?.
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?.
Solutions for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? defined & explained in the simplest way possible. Besides giving the explanation of
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?, a detailed solution for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? has been provided alongside types of Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? theory, EduRev gives you an
ample number of questions to practice Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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