Quadratic Equation Word Problem?

Question

A playground 40 meters wide by 60 meters long is to be doubled in area by extending each side an equal amount. By how much should each side be extended?

I thought I had this one in the bag, but the answer didn't check!
My equation was: (2x+60)(2x+40)=4800 but the answer I cam up with didn't check! Please help!

Answer 1

I think it should be (x+60)(x+40)=4800

So,
x^2+100x+2400=4800
x^2+100x-2400=0

(x+120)(x-20)=0

x=20..

so, it will be 60 meters wide and 80 meters long

Answer 2

To multiply an area by 2 you multiply length and width by √2 = 1.414. Check it:

l • √2 • w • √2 = 2lw = 2A.

So each side should be extended by 41.4%. Ah, but that would not be equal amounts, would it. So,

(60+x)(40+x) = 2(2400) = 4800
x² + 100x - 2400 = 0
(x + 120)(x - 20) = 0
discard negative solution, x = 20.

Check: (40+20)(60+20) = 60(80) = 4800.

Why'd you use 2x? Confusing area and perimeter?

Answer 3

isn't the equation (x+60)(x+40)=4800?

in that case, i would just guess and check, though i think there's a better way.

if x=30, 90*70=4800. No.

if x=25, 85*65=4800. No.

if x=20, 80*60=4800. Yes!

Each side would be extended 20 meters.

if you didn't want the answer (just help), then i can only say, oops. Sorry.

Answer 4

well.... you need to double the area. Knowing what the original area is might be a good first step.

A = Length * Width
so
A = 60 * 40 = 2400.

We want 2A, 2A = 4800.

We want to get to 2A by extending each side by an equal amount this gives: 2A = (L+x) * (W+x) or

2A = L*W+L*x+W*x+x^2

Now, solve for x.

2A = 2400+60x+40x+x^2
4800 = 2400 + 100x + x2
2400 = x^2+100x
0= x^2+100x - 2400

Now factor 2400. 120*20 works best and the equation factors as

0 = (x+120)*(x-20)

For this to zero out our two choices for x are x= -120 and 20. Since we can't add negative length our choice for x is 20 and we're done.

Answer 5

40*60=2400

(40+x) * (60+x)=4800

* = multiplies

If u want u can reverse the #s to say (x+40)(x+60)=4800

Answer 6

the first ONE Label the first consecutive huge style x Label the 2d one x+a million sq. of the first = x^2 decreased by using 25 = x^2 - 25 Equals 3 circumstances the 2d: x^2 - 25 = 3(x +a million)

Answer 7

I would go with Isabella. However, to check your answer, "FOIL" out your problem and solve with the quadratic formula. If you would like more help, please email me. I have no trouble at all.