document.write( "Question 621041: a rectangular room has an area of 60 ft^2.the width is 4 feet less than its length.find the width of the room.you don't have to draw a diagram. thanks. \n" ); document.write( "

Algebra.Com's Answer #390544 by matt501823(7) $\"\"$ $\"About$

You can put this solution on YOUR website!
You know that the surface area must be $\"60+ft%5E2\"$ . You also know that length times width equals the area, A. Thus you can say that $\"L%2AW=60\"$ , but you can also substitute in an alternate value for W since you know that width is 4 less than the length. Thus, we can now say $\"L%2A%28L-4%29=60\"$ this is the same as saying $\"L%5E2-4L=60\"$ (this was achieved by factoring). Now you can also say $\"L%5E2-4L-60=0\"$ . We can now factor this expression and can determine that $\"%28L-10%29%2A%28L%2B6%29=0\"$ . This means that either $\"L-10=0\"$ or that $\"L%2B6=0\"$ . If we solve for L-10=0 you get L=10; however if you solve for L+6=0 you get L=-6. Since you cannot have a negative length value the length must be 10 feet. Thus we can determine that the width must be 6 feet as $\"10-4=6\"$ . Now, let's double-check to make sure that our length and width values result in a surface area of $\"60+ft%5E2\"$ :
\n" ); document.write( " $\"10%2A6=60\"$
\n" ); document.write( " $\"60=60\"$
\n" ); document.write( "It works :) \n" ); document.write( "

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