Question

the length of a side of a square is 15 less than 4 times the length of a side of a second square. The perimeter of the two squares differ by 24 inches. Find in inches, the length of a side of the smaller square. Only an algebraic solution will be accepted

Answer 1

Oh yeah, first off, do you know how to write 15 less than 4 times the length of a side of a second square in algebraic form?

Answer 2

4x-15 ...?

Answer 3

Correct. :)

Answer 4

So to find the perimeter of any square, you do 4x, correct?

Answer 5

Yup.

Answer 6

Alright. So
4(4x-15) = ?
4(x) = ?

Answer 7

urm. 4x?

Answer 8

Great, 4(x) = 4x.
What about 4(4x-15) ?

Answer 9

16x-60=?

Answer 10

Great.
So you have 16x - 60 and 4x. Which side is greater? Well, pretend x is 2.
4 * 2 = 8
16(2) - 60 = -28.
Therefore, 4x is greater than 16x-60.

So, "The perimeter of the two squares differ by 24 inches."
The greatest perimeter subtract by the lowest perimeter = 24 inches.
or,
4x - 16x - 60 = 24.
Now simplify. :)

Answer 11

Which term can we combine?

Answer 12

4x-16x

-12x-60=24

-12x=84

x= -7 ...?

Answer 13

Indeed. I did something wrong. Wait a moment.

Answer 14

4x -(16x - 60)
= 4x - 16x + 60 = 24.
-12x + 60 = 24.
-12x = -36.
Make sense so far?
Divide both side by -12.

Answer 15

Arg. Let me think again.

Answer 16

Oh yeah, the square is not drawn to scale. >_>
So the bottom square is suppose to be bigger than the first square.

Answer 17

Blarg, too tired. Let Hero helped you. >_>
I mest up badly.

Answer 18

Aw kay.

Answer 19

Hold that thought. I got to go. Be back in 7-8 hrs. ): Thanks for helping tho ^_^

Answer 20

Lol. Be back in 7-8 hours...

Answer 21

f = length of side of first square
s = length of side of second square

f = 4s - 15


4(4s - 15) - 4s = 24

Answer 22

16s - 60 - 4s = 24
16s - 4s - 60 = 24
(16 - 4)s = 24 + 60
12s = 84
s = 84/12
s = 7

f = 4(7) - 15
f = 28 - 15
f = 13

Answer 23

Thank chu!