SOLUTION: The length of a rectangle is 3 times the width. The area is 108 cm^2. Find the dimensions of the rectangle.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The length of a rectangle is 3 times the width. The area is 108 cm^2. Find the dimensions of the rectangle.      Log On


   

Question 991004: The length of a rectangle is 3 times the width. The area is 108 cm^2. Find the dimensions of the rectangle.
Answer by ikleyn(52780) About Me  (Show Source):
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Let  x  be the length in centimeters,  and  y  be the width in centimeters.

You have two equations

system%28x+=+3y%2C%0D%0Axy+=+108%29.

Substitute the expression for  x  from the first equation to the second one.  You will get

3y%5E2 = 108,

y%5E2 = 108%2F3 = 36,

y = +/- 6.

Only positive value suits.  Thus the width is  6 cm.

Hence,  the length is 3*6 = 18 cm.

Check.  18*6 = 108 cm%5E2.