The perimeter of a rectangle is 52 inches, and its area is 168 in2. Find its length and width.

Question

anonymous · Answer

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so perimeter is 

2x+2y which equals 52 inches

2x+2y=52

area is xy and that equals 168

xy=168

now you have two unknowns, two equations, any idea what to do from here?

brinazarski · Answer

2x+(168/x)=52?

anonymous · Answer

looks good so far, keep going

brinazarski · Answer

2(x^2-26x+84)=0?

brinazarski · Answer

I think that's where I got lost last time I tried to solve this

brinazarski · Answer

I retried it and got x = sqrt(85) +13... but I'm doing this online and this problem says it's going to be rational number

anonymous · Answer

Just a second gonna do it on paper

brinazarski · Answer

Okay

anonymous · Answer

ohhh you left off the 2 thats why i got messed up. I shoulda looked at original problem. anyways,

2x+2(168/x)=52

2x+336/x=52

(2x^2/x)+(336/x)=52

(2x^2+336)/x=52

2x^2+336=52x

2x^2-52x+336=0

ok, see how i got this far?

brinazarski · Answer

Yup!

anonymous · Answer

factor out a two

2(x^2-26x+168)=0

now factor whichever way you like best

brinazarski · Answer

I got the answer from there :) Thank you so much!

anonymous · Answer

You're welcome