Two square rooms have a total floor area of 230 m2, and one is 4 metres bigger each way than the other. Let the smaller room have a length x. Find the dimensions of the room.

Please explain your answer

12.54m by 12.54 and 8.54m by 8.54m

Step-by-step 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

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