Question

6. Romeo is planning to elope with Juliet tonight. He knows that her windowsill is 18 feet from the ground. He also knows the 4-to-1 rule for using ladders which states that a ladder should be one foot away from the wall for each 4 feet he has to climb up the wall. He’s not sure if he will climb in to get her or if she will be waiting and he can grab
her and go. He has found these measurements on extension
ladders.
Which ladder would you recommend for Romeo to
Purchase to make all his dreams come true?
Be able to explain your answer.

Answer 1

Answer:

24' ladder

Step-by-step explanation:

It is sometimes useful to illustrate situations given in problems, as in this case;

The wall will be a vertical with a height 18 ft and the ladder will be away from the wall at the bottom and against the wall at the top end;

This is shown in the picture and as can be seen, it is a right-angle triangle;

We are told there is 4-to-1 rule, with which we can find the distance of the ladder from the wall at the bottom, denoted as a in the picture;

The rule is essentially saying the ratio of the vertical height of the ladder to the horizontal distance is 4 : 1, or ⁴/₁ (or just 4)

We know the vertical height of the ladder needs to be 18 ft since the window is that high up the wall;

The ratio will be 18 : a, or ¹⁸/ₐ

We can set the fractions equal to each other and solve:

¹⁸/ₐ = ⁴/₁

¹⁸/ₐ = 4

18 = 4a

a = 18/4

a = 4.5

The distance from the wall at the bottom should be 4.5 ft according to the 4-to-1 rule

Now we have the 2 sides of our triangles we can use Pythagoras theorem to find the length of the ladder, denoted x;

x² = (18)² + (4.5)²

x² = 324 + 20.25

x² = 344.25

x = 18.5539753

The ladder must be at least 18.6' long to be able to lean against the wall, reaching the window and complying with the 4-to-1 rule;

The ladder size therefore will be the 24' ladder, since it has a maximum length of 21' which can reach the window;

The smaller option, the 20', could be used since the reach is 19' 10", which is sufficient to reach Juliet but it would not likely be suitable for climbing into the window since it is not long enough;

Since he may climb into the window according to the scenario, the answer should be the 24' ladder both if he does or does not climb into the window;

I'm quite clueless about what to do with the information in the last 2 columns, not even sure what they mean to be honest so I think they are irrelevant.