An architect has allocated a rectangular space of 264ft^2 for a square dining room and a 10ft wide kitchen. What is both the width of the square dining room and the length of entire space.

Answer 1

width = x
length = y
kitchen is 10 by x
dining room is square so (y-10) = x

kitchen area = 10 x
dining area = x^2
so
10 x + x^2 = 264
x^2 + 10 x - 264 = 0
(x-12)(x+22) = 0
x = 12
y = x+10 = 22

so
living room is 12 by 12
length is 22