A few more math problems that I need help with

[IllusoryDeath]

Hello all.
To put it bluntly, I suck major balls in the math & geometry department.
A little help on these four problems, please?

1)


2)


3)


4)

[Eidolon]

I would solve the first one using the pythagorean theorem. There's probably an easier way, but I don't know one, so...


First, find the length of the red triangle's hypotenuse:

2^2 + 2^2 = x^2

Hidden stuff:

2.82842712

Now, since you know the length of that, you can use the ol' theorem once again on this triangle, marked in red:

Hidden stuff:

2^2 + 2.82842712^2 = 3.46410162^2

3.46410162 is the length of the diagonal.

Will probably help more after I go to dinner with my grandmother, if nobody beats me to it.

[IllusoryDeath]

Whoa....thank you, Eidolon. You even outlined the diagram thingy.
Your technique of explaining is really helping me out - I might just pass the upcoming test in a couple of days.

[Eidolon]

Quote:

Pythagoras sure is handy.

Find the length of segment DB or segment AC with the Pythagorean Theorem.
200^2 + 200^2 = DB^2

Hidden stuff:

DB = 282.842712

Cut it in half to find the length of the base of triangle EMB.

Hidden stuff:

141.421356

Now, instead of solving for the hypotenuse in the Pythagorean Theorem, we're solving for the vertical side, EM.

x^2 + 141.421356^2 = 200^2
x^2 + 20,000 = 40,000

Now get x by itself:

Hidden stuff:

x^2 = 20,000
x = 141.421356

EM = 141.421356 meters.

I fear that I have made this more complicated than it needed to be. Oh well.

Quote:

This one is simple.

To get the length of the shorter edge of the court:
8.23 + (1.37*2)

Hidden stuff:

10.97 meters

Double that, double 23.72, add those resulting values together. There's your perimeter.

Hidden stuff:

69.38 meters, if Google's calculator is correct.

And the answer to the second question will vary depending on what "marked lines" means.

It seems to me that it could be all the lines that were labeled with lengths, or it could be all the lines that are drawn on the court. I'm going to assume that they want the lengths of the lines drawn on the court.

23.72 + 23.72 + 8.23 + 8.23 + 6.40 + 6.40 =

Hidden stuff:

76.70 meters

Oh, and add the answer to the first question to that, if you feel that the perimeter is included in "marked lines."

Quote:

To find the perimeter of the lawn, we're going to subtract 16 from the answer to 16 + 16 + 10 + 10.

THIRTY-SIX!

And now we have to add one-quarter of the circumference of the four circles at the corners.

The radii of these circles are all 2 meters. So:

diameter = 4
circumference = pi * 4 = 12.5663706

And divide that by 4 to get the length of the round parts of the lawn.

Oh look! It turns out to be pi.

Oh look! We can just add 12.5663706 to THIRTY-SIX to get the perimeter of the lawn.

Hidden stuff:

48.5663706 meters

This question is sneaky, huh?

Anyway, the next question is simply a matter of multiplying the perimeter by 1000 to find its length in millimeters. We can then divide that number by 220 (the length of the bricks) to find out how many bricks it will take.

Hidden stuff:

perimeter = 48,566.3706 mm
number of bricks needed = 220.75623
2% wastage = 4.4151246

Add the wastage (number of bricks * 0.02) to the number of bricks needed and then round up to the nearest whole number. Answer to question number two right thar.

And total cost is simply 1.70 * answer to question number two.

Hidden stuff:

226 * 1.70 = $384.20

If I'm wrong, call me on it. Be angry about it, too.

[IllusoryDeath]

First & third equation set-ups were flawless, but the second one on the second part to the answer isn't coming up as being correct. The 'marked lines' thing is confusing for me, as well.... 76.70 meters wasn't right, and nor was 146.08 meters (the answer I got for adding that up with the first answer of 69.38). Do you think perhaps that the 'net' in the drawing is included in the equation, where it would be either 76.70+8.23+(1.37)2=87.67 meters or 146.08+8.23+(1.37)2=157.05 meters, depending on if the overall perimeter is included?

....

I tried both of those answers just now, and still neither are correct. Pretty sure that I did something wrong in that equation, and my brain is flashing the "WARNING: UTTERLY CONFUSED" signal, which usually means that I am about to smash the keyboard with my fists out of seething rage. Oh yes, the maths do that to me. :\ haha, but in no way am I angry at you: YOU are doing a smashing job of explaining things, truly.