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.
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
To find the width of the square dining room, we can use the formula for calculating the area of a square:
Area = side length^2
Let's assume that the width of the square dining room is denoted by "x" (in feet). Therefore, the area of the square dining room would be x^2.
Now, we know that the total area of the rectangular space is 240ft^2. Therefore, the area of the rectangular space can be expressed as the sum of the area of the square dining room (x^2) and the area of the kitchen (14 ft multiplied by the length of the rectangular space). Since the area of the kitchen is given by 14 * length, the total equation becomes:
240 = x^2 + 14 * length
To proceed, we need additional information or another equation.