Question 171883: A rectangular swimming pool has the length 30 m and width 20 m . There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write the quadratic equation to model this situation and use it to determine the width of the deck.
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! 30*20=600 m^2 is the pool area.
(30+2x)(20+2x)=2*600
600+40x+60x+4x^2=1,200
4x^2+100x+600-1,200=0
4x^2+100x-600=0
4(x^2+25x-150)=0
4(x-5)(x+30)=0
x-5=0
x=5 m. for the width of the deck.
Proof:
(30+10)(20+10)=1,200
40*30=1,200
1,200=1,200
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