SOLUTION: The length of a rectangular storage room is 8 f e e t l o n g e r t h a n i t s w i d t h . I f t h e a r e a o f t h e r o o m i s 1 0 5 s q u a r e f e

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Question 682982: The length of a rectangular storage room is 8 f e e t l o n g e r t h a n i t s w i d t h . I f t h e a r e a o f t h e r o o m i s 1 0 5 s q u a r e f e e t ,
find its dimensions.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The length L of a rectangular storage room is 8ft longer than its width W.
L=W%2B8ft............eq. 1
if the area A=L%2AW of the room is 105ft%5E2, than

105ft%5E2=L%2AW.........eq. 2....substitute L from eq. 1

105ft%5E2=%28W%2B8ft%29%2AW....solve for W

105ft%5E2=W%5E2%2B8Wft

W%5E2%2B8Wft-105ft%5E2=0

W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

W+=+%28-8ft+%2B-+sqrt%28+%288ft%29%5E2-4%2A1%2A%28-105ft%5E2%29+%29%29%2F%282%2A1%29+

W+=+%28-8ft+%2B-+sqrt%2864ft%5E2%2B420ft%5E2%29+%29%29%2F2+

W+=+%28-8ft+%2B-+sqrt%28484ft%5E2%29+%29%29%2F2+

W+=+%28-8ft+%2B-+22ft+%29%2F2+
find only positive root because the width cannot be negative
W+=+%28-8ft+%2B+22ft+%29%2F2+
W+=+14ft+%2F2+

highlight%28W+=+7ft%29+

now find the length L
L=W%2B8ft
L=7ft%2B8ft
highlight%28L=15ft%29