SOLUTION: (b) (l + 2) (l � 4) = 20 cm2, find l

Question 167792: (b) (l + 2) (l � 4) = 20 cm2, find l

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm replacing "l" with "x" (since "l" is often confused with 1)

Start with the given equation

FOIL

Subtract 20 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the possible answers are or

which approximate to or

Since we're looking for a measurement, and a negative measurement doesn't make much sense, this means that the only answer is which approximates to

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(L + 2) (L � 4) = 20 cm2, find L
------------
L^2-2L-8 = 20
L^2-2L-28 = 0
L = [2 +- sqrt(4-4*1*-28)]/2
L = [2 +- sqrt(116)]/2
L = [2 +- 2sqrt(29)]/2
L = 1+sqrt(29) or x = 1-sqrt(29)
===================================
Cheers,
Stan H.

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