SOLUTION: The area of a rectangle is 108 cm^2. the ratio of the width to the length is 3:4. Find the length and the width.

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Question 119183This question is from textbook Geometry
: The area of a rectangle is 108 cm^2. the ratio of the width to the length is 3:4. Find the length and the width. This question is from textbook Geometry

Answer by solver91311(24713) About Me  (Show Source):
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If the ratio of width to length is 3:4, then we can say that w%2Fl=3%2F4. Cross-multiplying gives 3l=4w or l=4w%2F3.

The area of a rectangle is given by A=lw. We know that the area is 108 square centimeters, so we can say: lw=108.

Now we can substitute 4w%2F3 for l

%284w%2F3%29w=108 or %284%2F3%29w%5E2=108

Multiply by 3/4:

w%5E2=81

w=9 (actually, w = plus or minus 9, but we can exclude the -9 result because we are looking for a positive number length measurement)

l=%284%2F3%29%289%29=12

So the width is 9 and the length is 12.