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Overtime
10-20-2010, 01:30 AM
Set up an equation and solve the problem.
The sum of the areas of two squares is 250 square inches. Each side of the larger square is three times the length of a side of the smaller square. Find the length of a side of each square.

Set up an equation and solve the problem.
A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 21 inches by 6 inches, in order to reduce the size of the paper to an area of 34 square inches. Find the width of the strip.

Help :(

I really need help with these type of equations. would be nice for a description on how you did it.

thanks

HyperSecret
10-20-2010, 01:45 AM
Side1 is 1 side of the 1st square
Side2 is 1 side of the 2nd square

Area of a square is Side*Side or Side^2

(Side1 * Side1) + (Side2 * Side2) = 250
3Side2 = Side1

This should solve the 1st question. Plug in for Side1 and solve.

(3Side2 * 3Side2) + (Side2)^2 = 250
9(Side2)^2 + (Side2)^2 = 250
10(Side2)^2 = 250
Side2 = Sqrt(25)
Side2 = 5

3Side2 = Side1
3(5) = Side1
15 = Side1

Check Solution:
(15*15) + (5*5) = 250
225 + 25
250 = 250

Correct

Overtime
10-20-2010, 01:49 AM
I have no idea what you are talking about :(

Whats with slide 1 and slide 2?

Do you mean it represents x?

holy crap i understand it now thanks :D

wait.. what if its the difference of 2 squares?

The difference of the areas of two squares is 1575 square feet. Each side of the larger square is eight times the length of a side of the smaller square. Find the length of a side of each square.

Get me started if you can, because i want to finish it. just tell me what to do.. :D

HyperSecret
10-20-2010, 02:07 AM
Same concepts, just a little different equations.

(Side1 * Side1) - (Side2 * Side2) = 1575
8Side2 = Side1

You can get it from here ;)

Overtime
10-20-2010, 02:11 AM
9(Side2)^2 + (Side2)^2 = 250
10(Side2)^2 = 250

what did you do to get 10? did you add +1?

cuz i did the same with 8 and now i have 64

HyperSecret
10-20-2010, 02:49 AM
yes, I added 1.

Its the same concept as 9x + x = 10x,

or 9x^2 + x^2 = 10x^2

Method
10-20-2010, 03:05 AM
sl = side of larger square
ss = side of smaller square
8ss = sl (given)

sl^2 - ss^2 = 1575 (using the information given)

substituting 8ss = sl, we get:

sl^2 - (1/8 * sl)^2 = 1575 (plugging in 8ss = sl, or ss = 1/8 * sl)

You can find the rest below this line if you get stuck or want to check your work.

sl^2 - 1/64 * sl^2 = 1575
64/64 * sl^2 - 1/64 sl^2 = 1575
63/64 * sl^2 = 1575
sl^2 = 1600
sl = 40 ft

ss = 1/8 * sl
ss = 1/8 * 40
ss = 5 ft

For the second one:

l = 21 in.
w = 6 in.
A = l * w

The problem says you're removing equal parts from both sides and both ends. We'll call the part you remove from one side x. Since you're removing from both sides and both parts, you're effectively removing 2x from both the length and width of the paper. Therefore, your new equation for the area looks like this:

A = (l - 2x) * (w - 2x)
A = (21 - 2x) * (6 - 2x)

We know the area of the new paper is going to be 34 in^2, so we can plug that in:

34 = (21 - 2x) * (6 - 2x)

I'll let you figure out the rest (though I'll leave it below for you to highlight again if you get stuck):

34 = 126 - 42x - 12x + 4x^2
4x^2 - 54x + 126 = 34
4x^2 - 54x + 92 = 0

Using the quadratic formula:

x = (54 +- sqrt((-54)^2 - 4(4)(92))) / 2(4)
x = (54 +- sqrt(1444)) / 8
x = (54 +- 38) / 8
x = (54 + 38) / 8 or x = (54 - 38) / 8
x = 11.5 or x = 2

Since the length of the smallest side (6) is less than 11.5, we can eliminate that answer. The correct answer is 2 in.

Overtime
10-20-2010, 05:14 PM
thanks guys.

Figured it out finally xD

I got it.

The larger was 40
and the smaller was 5.

40*40=1600
5*5=25

Subtract both.

Bam! =1575

for the 2nd one Method, im gettting -7/4.

My numbers changed on me on the assigment.

Its now 17x3 and 32 for the area

Method
10-20-2010, 07:21 PM
thanks guys.

Figured it out finally xD

I got it.

The larger was 40
and the smaller was 5.

40*40=1600
5*5=25

Subtract both.

Bam! =1575

for the 2nd one Method, im gettting -7/4.

My numbers changed on me on the assigment.

Its now 17x3 and 32 for the area

You can't remove a negative amount of paper, so a negative value makes no sense. You may be doing something odd in your calculations. And if the numbers change, just substitute those new numbers into the same equation:

A = l * w
32 = (17 - 2x) * (3 - 2x)
32 = 51 - 34x - 6x + 4x^2
4x^2 - 40x + 51 = 32
4x^2 - 40x + 19 = 0

Using the quadratic formula:

x = (40 +- sqrt((-40)^2 - 4(4)(19))) / 2(4)
x = (40 +- sqrt(1296)) / 8
x = (40 +- 36) / 8
x = (40 + 36) / 8 or x = (40 - 36) / 8
x = 9.5 or x = 0.5

Again, since you can't remove more paper from a side than is available, 9.5 doesn't make sense. The answer, therefore, is 0.5 inches from both sides and both parts.