Question

Two square rooms have a total floor of 89m^2.one room is 3m longer each way than the other,find the dimensions of the rooms

Answer 1

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 x ( x+4) = 45 

5m X 5m AND 8m X 8m 

5) x ( x+6) = 135 

x^2 +6x -135 = 0 

( x-9) ( x+15) = 0 

x = 9 

ANSWER 9 & 15

Answer 2

Answer:

Length of smaller square room is 5 m.

Length of bigger square room is 8 m.

Step-by-step explanation:

Sum of area of two squares room =$89 m^2$

Let the length of smaller square room be = x meter

Let the length of bigger square room be = x+3 meter

Are of square = $(Side)^2$

Area of bigger square room = A =$x^2 m^2$

Area of smaller square room= A'=$(x+3)^2 m^2$

$A+A'=89 m^2$

$x^2 m^2+(x+3)^2 m^2=89 m^2$

$x^2+x^2+9+6x=89$

$2x^2+6x-80=0$

$x^2+3x-40=0$

$x^2+8x-5x-40=0$

$x(x+8)-5(x+8)=0$

$(x+8)(x-5)=0$

x= -8, 5

Rejecting the negative value.

x = 5 m

Length of smaller square room = 5 m

Length of bigger square = (5 + 3 )m= 8 m