Adam has a hockey rink in his backyard. The current dimensions are 10m by 20m. Adam wants to have a hockey tournament and needs to double the area of his hockey rink. How much must Adam increase each dimension if he wants to increase them the same amount?

Current area = 200m2 [10m x 20m]

New area = 400m2 [10y x 20y]
So, 400 = 200y2
So, y2= 2
So, y = 1.41
So, each side must be increased by a factor 0f 1.41 times.
I this correct or do they mean add the same length to each side?

same to each

(10+x)(20+x) = 400
200 + 30 x + x^2 = 400

x^2 + 30 x - 200 = 0

x = [ -30 +/- sqrt(900 + 800) ]/2
x = [ -30 +/- 10 sqrt 17 ] /2
x = -15 +/- 5 sqrt 17
x = 5.62
new dimensions
15.62 * 25.62 = 400 ok

Hi Damon, I got the same answer as you up to the equation x^2 + 30x - 200=0, but after that I don't understand what happened after that.. where does the 900 and 800 come form? and why you do divide by 2? thanks

To double the area of the hockey rink, Adam needs to increase both dimensions by the same amount. Let's first find the current area of the hockey rink:

Area = Length × Width

Area = 10m × 20m

Area = 200 square meters

To double this area, Adam needs to increase it to 400 square meters. Since he wants to increase both dimensions equally, we can divide 400 by 2 to find the increased area for each dimension:

Increased area for each dimension = 400 square meters ÷ 2 = 200 square meters

Now, let's determine how much Adam must increase each dimension to achieve this increased area.

Let x be the amount Adam needs to increase each dimension.

The new length will be the current length plus x: 10m + x

The new width will be the current width plus x: 20m + x

The new area will be the product of the new length and the new width:

New Area = (10m + x) × (20m + x)

Since we want the new area to be 200 square meters, we can set up the equation:

(10m + x) × (20m + x) = 200

Expanding the equation:

200 + 10x + 20x + x^2 = 200

Combining like terms and moving 200 to the other side:

x^2 + 30x = 0

Now we can solve for x by factoring:

x(x + 30) = 0

So, x = 0 or x = -30

Since we're looking for a positive increase, we discard x = -30.

Therefore, Adam must increase each dimension by 0 meters to double the area of his hockey rink. This means the new dimensions will remain the same as the current dimensions: 10m by 20m.