Question 804186
x^2 is the dining area
11x is the kitchen
x^2+11x=312
x^2+11x-312=0
(x-13) (x+24) = 0
x=-24 Real life measurements can't be negative so disregard this result.
x = 13 ft 
13^2=169 sq ft is the area for the dining room
11*13 =143 sq ft is the area for the kitchen.