An architect has allocated a rectangular space of 240ft^2 for a square dining room and a 14 ft wide kitchen. Find both the width of the square dining room and the length of the entire rectangular space.

Answer 1

As you can see from the many similar questions, this poorly worded question comes up again and again with just a change of numbers

We must assume that the width is the same for the kitchen and the dining room

let the dining room be x by x
area of dining room = x^2
area of kitchen = 14x

x^2 + 14x = 240
x^2 + 14x - 240 = 0
(x-10)(x+24) = 0
x = 10 or x = -24, which of course would be inadmissible

the dining room is 10 by 10, the kitchen is 10 by 14
and the length of the whole space is 24