the ride is in the shape of a rectangle with dimensions 3 m by 8 m. it is to be doubled in area by adding a single strip to the length and width of rectangle

Question

Calculate the new dimensions of the pool

Answer 1

The original area is 3m * 8m = 24 m²

 

I assume the strip is the same measure across on each?  If so, 

 

(3 + x)(8 + x) must be 2(24)

 

24 +8x + 3x + x² = 48  re-writing

 

x²+ 11x - 24 = 0

 

x = [-11 ±√(121 + 96)] /2

 

 = (-11 ± √217 )/2

 

 =  (-11 + 14.7309)/2  and  (-11 - 14.7309)/2

 

 = 3.731/2 = 1.865 m  and something negative.  Width cannot be negative - so ignore the 2nd answer.

 

3 + 1.86546 m by 8 + 1.86546 m  = 4.86546m x 9.86546 m are the new dimensions.

 

 

Now, let's check that by finding the new area.

 

4.86546 m x 9.86546 m = 48.0000010116 m²

 

That looks pretty much like 48 to me!