Question

An architect has allocated a rectangular space of 589ft^2 for a square dining room and a 12ft wide kitchen. Find both the width of the square dining room and the length of the entire rectangular space.
The width of the square dining room is _____ft
The length of the entire rectangular space is ____ft.

Answer 1

I am going to assume that the kitchen and the dining room have the same width.

so the length of large rectangle is x+12
and the width is x
so x(x+12) = 589
x^2 + 12x = 589
x^2 + 12x + 36 = 589+36
(x+6)^2 = 625
x+6 = ± √625 = ± 25
x = -6 + 25 or -6-25 , the last answer is inadmissible

x = 19

large room is 19 by 31

check:
19 x 31 = 589