SOLUTION: A rectangular skating rink measures 40 m by 20 m. Next year the rink is to be doubled in area by extending each side by the same amount. Determine how much each side should be ex

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A rectangular skating rink measures 40 m by 20 m. Next year the rink is to be doubled in area by extending each side by the same amount. Determine how much each side should be ex      Log On


   

Question 210974: A rectangular skating rink measures 40 m by 20 m. Next year the rink is to
be doubled in area by extending each side by the same amount. Determine how
much each side should be extended, to the nearest tenth of a meter.
Found 2 solutions by Earlsdon, MathTherapy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The present area is:
A+=+40%2A20sq.m.
A+=+800sq.m. If you add x to the width and this doubles the area, you have:
1600+=+40%2820%2Bx%29 Divide both sides by 40.
40+=+20%2Bx Subtract 20 from both sides.
20+=+x
The sides must be extended by 20 meters.

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular skating rink measures 40 m by 20 m. Next year the rink is to
be doubled in area by extending each side by the same amount. Determine how
much each side should be extended, to the nearest tenth of a meter.

Let the amount that each side will be extended by be x

Then we'll have: (40 + x)(20 + x) = 2(800)

800+%2B+60x+%2B+x%5E2+=+1600
x%5E2+%2B+60x+-+800+=+0

Since this cannot be easily factored, we use the quadratic equation to solve

a = 1 ; b = 60 ; c = - 800
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-60+%2B-+sqrt%28+60%5E2-4%2A1%2A-800%29%29%2F%282%2A1%29

x+=+%28-60+%2B-+sqrt%283600+%2B+3200%29%29%2F2
x+=+%28-60+%2B-+sqrt%286800%29%29%2F2
x+=+%28-60+%2B+82.46%29%2F2 or x+=+%28-60+-+82.46%29%2F2
Ignore x+=+%28-60+-+82.46%29%2F2 as measurement CANNOT be a negative number
Therefore, x+=+%28-60+%2B+82.46%29%2F2 = x+=+%2822.46%29%2F2 = 11.23

Each side needs to be extended highlight_green%2811.2%29 meters.

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Check
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(40 + 11.2)(20 + 11.2) = 51.2 * 31.2 = 1,597.44, which is approximately 1,600 meters, or twice 800 meters.