SOLUTION: When the width is (n+2) the height is 3 less than (n+2) and the area is 119 what is n?

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Question 912108: When the width is (n+2) the height is 3 less than (n+2) and the area is 119 what is n?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

When the width is W=+%28n%2B2%29+ the height (or length) is 3 less than W=%28n%2B2%29, the L=W-3=+%28n%2B2%29-3
and the area is A=119
solution:
A=L%2AW
A=%28%28n%2B2%29-3%29%2A%28n%2B2%29

119=%28n%2B2-3%29%2A%28n%2B2%29 ...solve for n
119=%28n-1%29%2A%28n%2B2%29
119=n%5E2%2B2n-n-2
0=n%5E2%2Bn-2-119
n%5E2%2Bn-121=0

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

n+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-121%29+%29%29%2F%282%2A1%29+
n+=+%28-1+%2B-+sqrt%28+1%2B484%29%29%2F2+

n+=+%28-1+%2B-+sqrt%28+485%29%29%2F2+
n+=+%28-1+%2B-+22.02271554554524+%29%2F2+

solutions:
n+=+%28-1+%2B+22.02271554554524+%29%2F2+
n=21.02271554554524%2F2
n=10.51135777277262 ....since we dealing with width and length, we need only positive solution


the width: W=%28n%2B2%29 => W=%2810.51135777277262%2B2%29 =>W=12.51135777277262
the length: L=W-3=+12.51135777277262-3 => L=+9.51135777277262
A=L%2AW => 119=9.51135777277262%2A12.51135777277262 =>119=119