SOLUTION: rectangle with perimeter 20cm length xcm diagonal 8cm show x^2 - 10x +18 = 0

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Question 747317: rectangle with perimeter 20cm
length xcm
diagonal 8cm
show x^2 - 10x +18 = 0
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

rectangle with perimeter 2x%2B2%2AW=20cm where W is the width and
x is the length
if diagonal d=8cm then d%5E2=W%5E2%2Bx%5E2 => 64cm%5E2=W%5E2%2Bx%5E2
2x%2B2%2AW=20cm..eq.1...solve for x..divide all terms by 2

x%2BW=10cm
x=10cm-W.....plug in 64cm%5E2=W%5E2%2Bx%5E2
64cm%5E2=W%5E2%2B%2810cm-W%29%5E2......solve for W
64cm%5E2=W%5E2%2B100cm%5E2-20W%2BW%5E2
2W%5E2-20W%2B100cm%5E2-64cm%5E2=0
2W%5E2-20W%2B36cm%5E2=0.....divide all terms by 2
W%5E2-10W%2B18cm%5E2=0
W+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A18+%29%29%2F%282%2A1%29+
W+=+%2810+%2B-+sqrt%28100-72+%29%29%2F2+
W+=+%2810+%2B-+sqrt%2828%29%29%2F2+
W+=+%2810+%2B-+sqrt%284%2A7%29%29%2F2+
W+=+%2810+%2B-+2sqrt%287%29%29%2F2+
W+=5+%2B-+sqrt%287%29+
so, W+=5+%2B+sqrt%287%29=7.65cm+ or W+=5+%2B+sqrt%287%29=2.35cm+
now find x
x=10cm-W
x=10cm-7.65cm=2.35cm or x=10cm-2.35cm=7.65cm

so, we will take the length highlight%28x=7.65cm%29 and the width highlight%28W+=2.35cm%29+

now show x%5E2+-+10x+%2B18+=+0
%287.65%29%5E2+-+10%2A7.65+%2B18+=+0
58.5225+-+76.5+%2B18+=+0
58.5%2B18+-+76.5+=+0
76.5+-+76.5+=+0
0=+0