The gilbert's are designing a rectangular patio. the patio has an area of 432 square feet. the width of the patio is 3/4 it's length. what is the length of the patio

Represent the unknowns. 
Let x = length 
since the width is 3/4 of the length, 
Let (3/4)x = width 

Recall that the area of rectangle is just width multiplied by the length, 
A = w * l 
Substituting, 
432 = (3/4)x * x 
432 = (3/4)x^2 
432 * 4/3 = x^2 
576 = x^2 
Get the square root of both sides, 
x = 24 feet (length) 

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