Question 951917: The length of a rectangular room is 5 yd more than the width. If the area is 300 yd2, find the length and the width of the room.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let's call width "w", and the length "l" is w+5. Formula for the area is w*l:
w*(w+5) = 300 Multiply on the left:
w^2 + 5w = 300 Subtract 300 from both sides, and I'm going to rearrange the terms:
-300 + 5w + w^2 = 0 Factor and you get:
(-20 + -1w)(15 + -1w) = 0 Now we have two equations, let's solve for each:
-20 + -1w = 0 and 15 + -1w = 0 Solve the first equation:
-20 + -1w = 0 Add 20 to both sides:
-1w = 20 Divide both sides by -1:
w = -20
Now second equation:
15 + -1w = 0 subtract 15, both sides
-1w = -15 Divide both sides by -1:
w = 15
Our answer is w = {-20, 15} Since -20 is negative we cannot use it. Our answer has to be 15 for the width, And the length is 5 more:
Proof: 15 x (15 + 5) = 15 x 20 = 300 Our answer is correct.
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