Divide a straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. (i) Let AB be the given straight line. It is required to divide it internally in K, so that AK2 = AB BK. On AB describe square ACDB. Bisect AC in E. Join EB and produce CA to G making EGEB. On AG describe square AGHK, then K is the required point. Produce HK to L [Fig. 59 (i)]. G H K' A B K B A E D E C G D
Divide a straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. (i) Let AB be the given straight line. It is required to divide it internally in K, so that AK2 = AB BK. On AB describe square ACDB. Bisect AC in E. Join EB and produce CA to G making EGEB. On AG describe square AGHK, then K is the required point. Produce HK to L [Fig. 59 (i)]. G H K' A B K B A E D E C G D
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.CT: Test
Problem 1CT: Complete each statement. a Given that the length and the width of a rectangle are measured in...
Related questions
Question
![Divide a straight line into two parts, so that the rectangle contained by
the whole and one part may be equal to the square on the other part.
(i) Let AB be the given straight line. It is required
to divide it internally in K, so that AK2 = AB BK. On AB describe
square ACDB. Bisect AC in E. Join EB and produce CA to G making
EG EB. On AG describe square AGHK, then K is the required
point. Produce HK to L [Fig. 59 (i)].
G
H
A
B
K
A
E
B
D
E
C
D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8547368d-61ae-448e-997c-bb66faf12143%2F2afb4f9d-6479-495b-9013-0a8a6cff434b%2F7zgn1wd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Divide a straight line into two parts, so that the rectangle contained by
the whole and one part may be equal to the square on the other part.
(i) Let AB be the given straight line. It is required
to divide it internally in K, so that AK2 = AB BK. On AB describe
square ACDB. Bisect AC in E. Join EB and produce CA to G making
EG EB. On AG describe square AGHK, then K is the required
point. Produce HK to L [Fig. 59 (i)].
G
H
A
B
K
A
E
B
D
E
C
D
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning