Answer:
12.54m by 12.54 and 8.54m by 8.54m
Explanation:
Area of a square = L²
L is the side length of the room
The total area of the two square room = A₁+A₂
T = A₁+A₂
T = L₁²+x²
If the two square rooms have a total floor area of 230 m², then;
L₁²+x² = 230. ..... 1
If one room is 4 meters bigger each way than other, then;
L₁ = x + 4 .... 2
where x is the length of the smaller room
Substitute equation 2 into 1;
From 1: L₁²+x² = 230
(x+4)²+x² = 230
x²+8x+16+x² = 230
2x²+8x+16-230 = 0
2x²+8x-214 = 0
x²+4x-107 = 0
x = -4±√16-4(-107)/2
x = -4±√16+428/2
x = -4±21.07/2
x = 17.07/2
x = 8.54m
L₁ = x+4
L₁ = 8.54+4
L₁ = 12.54m
Hence the dimensions of the room is 12.54m by 12.54 and 8.54m by 8.54m