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YanaSidlinskiy
 one year ago
The area of a rectangular garden is 54 square meters. The width is 7 meters longer than onethird of the length. Find the length and the width of the garden. Use the formula, are = length * width.
YanaSidlinskiy
 one year ago
The area of a rectangular garden is 54 square meters. The width is 7 meters longer than onethird of the length. Find the length and the width of the garden. Use the formula, are = length * width.

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438819879525:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The width is 7 meters longer than onethird the length, so we can say \[\Large W = \frac{1}{3}L + 7\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The area of the rectangle is length * width, so \[\Large A = L*W\] \[\Large 54 = L*\left(\frac{1}{3}L + 7\right)\] Do you see how to solve for L from here?

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. Would it be \[54=\frac{ 1 }{ 3 }x^2+7x\] From there I need help...

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what I would do from there is multiply everything by 3 to get rid of the fraction

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then get everything to one side

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1So like multiply 1/3x^2(3) and multiply 7x(3)?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah and 54 as well

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Got it. Would it be: \[162=1x^2+21x\]

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Or instead I should just put \[x^2\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now move that 162 over

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I have a question... Does it matter with what number I multiply the numbers with?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you mean like how you multiplied everything by 3 just now?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The denominator of the fraction was 3, so multiplying everything by that clears out the denominator (ie eliminates the fraction)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if you picked another number that wasn't a multiple of 3, then the denominator or fraction wouldn't go away

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Oh ok! Gotcha! Ok. So I got: 1x^2+21x162=0 Give me a sec. I wanna do it myself and you tell me what I got wrong.

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1I got: (x+54)(x3) PLEASE tell me it's right haha! I've had so much trouble with this today.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.154 times 3 = 162 .... true 54 plus 3 = 21 ... false so that's not the correct factorization

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1I'm confused and I think this is the stop. So how would I know which number goes where? Or more like why does it matter where I put down the sign with which number?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The quadratic formula may be easier to work with. Did you want to use that?

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, I wanna use that instead... This is really hard for me and I have no idea why...

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Ok, let me figure it out using the quadratic formula.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.11x^2+21x162 means a = 1 b = 21 c = 162 plug those values into \[\Large x=\frac{b \pm \sqrt{b^24ac}}{2a}\]

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1I'm not exactly sure if this is right, but so far I have: \[x=\frac{ 21\pm \sqrt{207} }{ 2 }\] Is that right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The 207 portion is incorrect b^2  4ac = 21^2  4*1*(162) = 1089

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1So I multiplied it incorrectly? How?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.121^2 = 441 4*1*(162) = 648

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.121^2  4*1*(162) = 441  (648) = 1089

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Ahh! That's what I was missing! Gotcha! Ok. Hang on:)

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1So it'd be like \[x=\frac{ 21\pm \sqrt{1089} }{ 2 }\] ?

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Sorry for making you wait.... I'm kinda slow on thinking right now...

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1You're doing great. Don't worry.

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1I hope so... So my answer would be x=534?

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1The answer can never be negative.. I know that...

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Ughgh. Ok, I need some real help. What is it?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large x=\frac{ 21\pm \sqrt{1089} }{ 2 }\] \[\Large x=\frac{ 21+ \sqrt{1089} }{ 2 } \ \text{ or } \ x=\frac{ 21 \sqrt{1089} }{ 2 }\] \[\Large x=\frac{ 21+ 33 }{ 2 } \ \text{ or } \ x=\frac{ 21 33 }{ 2 }\] \[\Large x=?? \ \text{ or } \ x=??\]

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Wow, ok. I divided 1089 by 2 so that's what threw me off... Hang on let me get the final answer..

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1x took the place of the length L so L = 6 or L = 27 but a negative length makes no sense which is why we ignore 27

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1So, what would be my width? I don't seem to be understanding that part..

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1go back to \[\Large W = \frac{1}{3}L + 7\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug in L = 6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1or you can ask yourself "something times 6 gives the area of 54, what is that something?"

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Oh yeah. Sorry. I'm like dead tired and didn't get enough sleep lol.. 9

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep L = 6 and W = 9

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Anyways, THANK YOU SO MUCH!!!!!! I can't appreciate you enough. I'd be sitting behind the computer sending you billions of messages with different thank you's. Thanks again!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'm glad it's making sense now

YanaSidlinskiy
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, me too. I have another one similar to this, but I'll figure it out myself and let you check it since it's coming to my brain lol. Anyways, just expect a "check message" from me or something...

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok sounds like a good plan to me
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