SOLUTION: A rectangle 15cmx30cm is increased on all sides by the same amount. It's area is increased by 144cm^2. By how much is each dimension increased?

Algebra ->  Rectangles -> SOLUTION: A rectangle 15cmx30cm is increased on all sides by the same amount. It's area is increased by 144cm^2. By how much is each dimension increased?      Log On


   

Question 636311: A rectangle 15cmx30cm is increased on all sides by the same amount. It's area is increased by 144cm^2. By how much is each dimension increased?
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
Increase on all sides = x

Area of rectangle = length * width
A=L*W
A=15*30
A=450
After Increase
A=450+144
A=594
Length = 30+x
Width = 15+x
594=(15+x)(30+x)
594=450+15x+30x+4x^2
594=450+45x+x^2
594-450=45x+x^2
144=45x+x^2
x^2+45x-144=0
x^2+48x-3x-144=0
x(x+48)-3(x+48)=0
(x-3)(x+48)=0
x-3=0 or x+48=0
x=3 or x=-48 (unacceptable)
x=3


Each dimension increased by 3cm
Length = 30+x = 30+3 = 33cm
Width = 15+x = 15+3 = 18cm