Question 636311
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