SOLUTION: The length of a rectangle is 3 inches more than the width. The area of the rectangle is 154 inches. Find the width of the rectangle.

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Question 289094: The length of a rectangle is 3 inches more than the width. The area of the rectangle is 154 inches. Find the width of the rectangle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = length and W = width

Since "The length of a rectangle is 3 inches more than the width", we know that L=W%2B3 (just add 3 to the width to get the length). Furthermore, we're given that "The area of the rectangle is 154 inches", so we can say that 154=LW (recall that the area of a rectangle is A=LW, multiply the length and width to get the area).



So we have the two equations: L=W%2B3 and 154=LW


154=LW Start with the second equation.


154=%28W%2B3%29W Plug in L=W%2B3. In other words, replace each "L" with "W+3". Notice how the "L" terms are now gone and we now have an equation with one variable.


154=W%28W%2B3%29 Rearrange the terms.


154=W%5E2%2B3W Distribute.


0=W%5E2%2B3W-154 Subtract 154 from both sides.


0=%28W%2B14%29%28W-11%29 Factor the right side.


W%2B14=0 or W-11=0 Use the zero product property.


W=-14 or W=11 Solve for 'W' in each equation.


So the two possible solutions for 'W' are W=-14 or W=11. However, since we can't have a negative width, the only solution is W=11.


So the width is 11 inches. Now just plug this value into L=W%2B3 to get L=W%2B3=11%2B3=14. So the length is 14 inches.


Take note that the length is indeed more than width and that 11*14=154 which verifies our answer.