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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A rectangular skating rink measures 40m by 20m. It is to be doubled in area by extending each side by the same amount. Determine how much each side should be extended, to the nea      Log On


   

Question 186014: A rectangular skating rink measures 40m by 20m. It 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 x be the amount that each side is extended in meters.
(40 + 2x)(20 + 2x) = 40*20*2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular skating rink measures 40m by 20m. It 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.
:
Original area: 40 * 20 = 800 sq/m
New area: 2 * 800 = 1600 sq/m
;
Let x be the amount that each side is extended in meters.
(x+40) * (x+20) = 1600
FOIL
x^2 + 20x + 40x + 800 = 1600
;
x^2 + 60x + 800 - 1600 = 0
A quadratic equation:
x^2 + 60x - 800 = 0
Use the quadratic formula to solve for x:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem; a=1, b=60, c=-800
x+=+%28-60+%2B-+sqrt%2860%5E2+-+4%2A1%2A-800+%29%29%2F%282%2A1%29+
x+=+%28-60+%2B-+sqrt%283600+-+%28-3200%29+%29%29%2F2+
x+=+%28-60+%2B-+sqrt%283600+%2B+3200+%29%29%2F2+
x+=+%28-60+%2B-+sqrt%286800+%29%29%2F2+
Two solutions, but only the positive solution interests us here;
x+=+%28-60+%2B+82.462%29%2F2+
x = 22.462%2F2
x = 11.23, rounded to nearest tenth; 11.2 m added to each dimension
;
:
Check the solution, add this to each original dimension, and find the area:
51.23 * 31.23 = 1599.9 ~ 1600