Question

the width of the mirror is 4/9 it's lenght the area of the mirror is 576 sq in. what are the dimension s of the mirror

Answer 1

Area = L(ength) x W(idth) 
W = 4/9L 

You just need to plug in the numbers into the area formula and solve
576 = L × 4/9L 
576 = 4/9L²                 (combining the two variables since they are the same)
(9/4) 576 = 4/9L² (9/4)           (isolating L²) 
1296 = L² 
√1296 = √L²           (isolating L by removing the square. √ is the opposite of ²) 
36 = L 

Since we know 36 is L now we need to find W (using the formula we made)
W = 4/9L 
W = 4/9(36)
W=16 

The dimensions of the mirror are 36 in. x 16 in.

Answer 2

Suppose the length is x and the width is 4/9x and the whole mirror is 4/9x*x=576
or 4/9(x^2)=576 first divide both sides by 4/9
x^2=16 solve for x
x=4