SOLUTION: A room has an area of 322 square feet. one dimension is 9ft more than the other. Find the dimensions of the room?

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Question 247312: A room has an area of 322 square feet. one dimension is 9ft more than the other. Find the dimensions of the room?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Let us see the room (being rectangle):


Area%5BR%5D=L%2AW=%28x%2B9%29%28x%29
322ft%5E2=x%5E2%2B9x
x%5E2%2B9x-322=0, wheresystem%28a=1%2Cb=9%2Cc=-322%29
Solving discriminant:
b%5E2-4ac=9%5E2-4%281%29%28-322%29=81%2B1288=1369

Continuing the quadratic eqn:
x=%28-9%2B-sqrt%281369%29%29%2F%282%281%29%29
x=%28-9%2B-37%29%2F2
2 values:
x=%28-9%2B37%29%2F2=28%2F2=red%2814ft=Width%29, use (Answer)
x=%28-9-37%29%2F2=-46%2F2=-23, discard
Length: 9%2B14=red%2823ft%29
Check,
A=L%2AW
322ft%5E2=%2823%29%2814%29
322ft%5E2=322ft%5E2

Thank you,
Jojo