Question

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?

Answer 1

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?

Answer 2

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

Answer 3

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