# Case Study Question 03

## Chapter 11: Constructions

### Class 10

Linking San Francisco with Marin County, the Golden Gate Bridge is a 1.7 mile-long suspension bridge that can be crossed by car, on bicycles or on foot. The Golden Gate Bridge, completed after more than four years of construction, is a landmark recognized almost universally. The Golden Gate Bridge’s 4,200-foot-long main suspension span was a world record that stood for 27 years. The bridge’s two towers rise 746 feet making them 191 feet taller than the Washington Monument. The five-lane bridge crosses Golden Gate Strait.

Question.1.
To divide a line segment AB in the ratio m:n (m, n are positive integers), we draw a ray AX so that \angleBAX is an acute angle and then mark points on ray AX at equal distances. What will be the minimum number of these points?

As we want to divide the given line segment in the ratio m:n, we mark (m + n) points at equal distances on the ray AX drawn as given in the question. This is because we will use Basic proportionality theorem in dividing the line segment in the ratio m : n by joining A_{m+n} to B and then drawing a line through A_{m} parallel to A_{m+n}B to intersect AB at C. Then AC : CB = m:n (By BPT). Hence the minimum number of points will be m+n.

Question.2.
Suppose we want to divide the main suspension span of the bridge, which is 4200 feet long, in the ratio 3:4. What will be the minimum number of points which should be marked on ray AX.

As we want to divide the given line segment in the ratio 3:4, we mark 7 (3 + 4) points at equal distances on the ray AX drawn as given in the question. This is because we will use Basic proportionality theorem in dividing the line segment in the ratio 3:4 by joining A to B and then drawing a line through A_{3} parallel to AB to intersect AB at C Then AC : CB = 3:4 (By BPT). Hence the minimum number of points to be marked are 7.

Question.3.
In the above question, points A_{1}, A_{2}, A_{3}, … are located at equal distances on the ray AX drawn such that \angleBAX is an acute angle. To which point should point B joined to?

We will use Basic proportionality theorem in dividing the line segment in the ratio 3:4 by joining A_{7} to B and then drawing a line through A_{3} parallel to A_{3}B to intersect AB at C. Then AC : CB = 3:4 (By BPT).
Hence, the point joined should be A_{7}.

Question.4.
What is the principal theorem or rule used in the steps to divide the given line segment in any ratio?

Basic Proportionality Theorem.

Question.5.
In the part (B), suppose a ray AX is drawn such that \angleBAX is an acute angle. Then a ray BY is drawn parallel to AX and the points A_{1}, A_{2}, A_{3}, … and B_{1}, B_{2}, B_{3}, … are located at equal distances on ray AX and BY, respectively. Then which two points will be joined together?

A_{3} and B_{4} will be joined together.

error: Content is protected !!