SOLUTION: A rectangle has an area of 60m squared . If the length and the width are each increased by 2m, the area is doubled.Find the dimensions of the original rectangle correct to one

Algebra ->  Rectangles -> SOLUTION: A rectangle has an area of 60m squared . If the length and the width are each increased by 2m, the area is doubled.Find the dimensions of the original rectangle correct to one       Log On


   

Question 1021231: A rectangle has an area of 60m squared . If the length and the width are each increased by 2m, the area is doubled.Find the dimensions of the original rectangle correct to one decimal place.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.L%2AW=60
2.%28L%2B2%29%28W%2B2%29=2%2A60=120
From 1,
W=60%2FL
Substituting,
%28L%2B2%29%2860%2FL%2B2%29=120
60%2B2L%2B120%2FL%2B4=120
2L%2B120%2FL=56
Multiply by L,
2L%5E2%2B120=56L
2L%5E2-56L%2B120=0
L%5E2-28L%2B60=0
L%5E2-28L%2B196%2B60=196
%28L-14%29%5E2=136
L-14=0+%2B-+sqrt%28136%29
L=14+%2B-+sqrt%28136%29
L=14+%2B-+4sqrt%2837%29
To find W,
W=60%2FL
W=60%2F%2814%2B-4sqrt%2837%29%29
W=14%2B-+4+sqrt%2837%29 interchanging +-.
So,
L=14%2B4sqrt%2837%29,W=14-4sqrt%2837%29
or
L=14-4sqrt%2837%29,W=14%2B4sqrt%2837%29