SOLUTION: Several questions (2) 1) An outoor ropes course includes a cable that is connected between 2 trees; trees are 24 ft. apart. Cable slopes down from a height of 35 ft. on one tr

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Question 325772: Several questions (2)
1) An outoor ropes course includes a cable that is connected between 2 trees; trees are 24 ft. apart. Cable slopes down from a height of 35 ft. on one tree to a height of 25 ft. on the other tree. How long is the cable?
- I do not even know how to approach; attempted to visualize and set up equation as area of triangle where base is 24 ft and height is 35 ft.????

2) Find the total area of rectangles: 1st rectangle L=3; W=3;
2nd rectangle L = 4x; W=4x
my answer: since A = LW; (4x + 3)^ where ^ is 2; so based on that reasoning, answer is 4x^ +24x + 9 (re: ^ is 2).
I appreciate any and all assistance; thank you.

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
# 1

Hint: If you draw the picture, you get

From there, use the pythagorean theorem to solve for 'x' (use , and )
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# 2

Area of first rectangle: 3*3=9

Area of second rectangle:

Total area: (just add the two individual areas)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Please read the instructions on the page where you submit your questions. It is rather clear that you should only ask one question per submission.

1. You are on the right track with the idea of a triangle. But the height of the triangle is the DIFFERENCE of the heights of the ends of the cable. 35 minus 25 is 10. So you have a right triangle with legs of 10 and 24. Use Pythagoras to calculate the hypotenuse. (check your work by comparing your answer to a 5-12-13 Pythagorean triple)

2. The area of the first square is 3 times 3 is 9. The area of the other is 4x times 4x is . The sum is .

is the area of a square that measures on a side and which is exactly square units larger than the sum of the areas of your original two squares.

A couple of other things:

x^ does NOT represent . The caret mark means raise the thing that precedes the caret mark to the power of the thing that comes after it. If you want to say , write x^2. If you want to say , write x^3, and so on.

John