Question

Joe has a rectangular patio that measures 10 feet by 12 feet. he wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. which equation could be used to determine x?

Answer 1

We know that

step 1
find the original area of rectangle

Area of rectangle=L*W-----> 10*12----> 120 ft²

step 2
find the new area
if increase the area by 50%
so 
the new area=120*1.5----> 180 ft²

step 3
find the new dimensions
(10+x) ft x (12+x) ft
new area=(10+x)*(12+x)
180=(10+x)*(12+x)----> 180=120+10x+12x+x²----> 180=x²+22x+120
x²+22x-60=0

using  a graph tool-----> to resolve the second order equation
see the attached figure
the solution is
x=2.454 ft

the answer 
the equation is
$x^{2} +22x-60=0$