SOLUTION: the length of the top of a table is 6m greater then the width. the area is 72m(to the second). find the dimensions of the table wdth? length?

Algebra ->  Rectangles -> SOLUTION: the length of the top of a table is 6m greater then the width. the area is 72m(to the second). find the dimensions of the table wdth? length?      Log On


   

Question 595166: the length of the top of a table is 6m greater then the width. the area is 72m(to the second). find the dimensions of the table
wdth?
length?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = width

Since "the length of the top of a table is 6m greater then the width", we know that the length is x+6

The area is then x(x+6), but this area is 72 sq meters, so


x%28x%2B6%29+=+72


Now get the equation into standard form


x%28x%2B6%29+=+72


x%5E2%2B6x+=+72


x%5E2%2B6x+-+72=0


and now use the quadratic formula to solve for x.


x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%286%29%2B-sqrt%28%286%29%5E2-4%281%29%28-72%29%29%29%2F%282%281%29%29

x+=+%28-6%2B-sqrt%2836-%28-288%29%29%29%2F%282%29

x+=+%28-6%2B-sqrt%28324%29%29%2F2

x+=+%28-6%2Bsqrt%28324%29%29%2F2 or x+=+%28-6-sqrt%28324%29%29%2F2

x+=+%28-6%2B18%29%2F2 or x+=+%28-6-18%29%2F2

x+=+12%2F2 or x+=+-24%2F2

x+=+6 or x+=+-12

Discard the negative solution to get the only solution of x=6

So the width is x = 6 meters

and the length is x + 6 = 6+6 = 12 meters


As a check, notice that 12 is indeed 6 greater than 6. Also 12*6 = 72. So our answers check out.