The area, A is 180 units.

The area A = length times width = L * W

but since the length, L, is 3 more than the width, W (or the width plus 3). So L is bigger than W, right???

so use L = (W + 3)

now look at the area formula again and use algebra.

You can't solve for two different variables with only one equation. But if you replace the L with (W + 3), you only have one variable and one equation - that we can do!

So A = 180 = L * W = (W + 3) * W

which is the same as: 180 = W * (W + 3) or simply W(W + 3) = 180

next W^{2} + 3W = 180 (by using the distributive property to multiply)

make it into a quadratic equation by subtracting 180 from both sides:

now we get W^{2} + 3W -180 = 0, try to solve by factoring: (W + ?)(W - ??) = 180

so those question marks will be numbers. what 2 numbers multiply to -180 and add up to 3?

so they are close to each other but one is negative.

try 18*-10, close but not it.

try 15*something next. 180/15=12

so 15*-12 works!

so now (W + 15)(W - 12) = 0

set each part equal to 0 and solve. so W + 15 = 0, so W = -15units??? is that realistic?

or W - 12 = 0, so W = 12. That looks good!

and since the length is 3 more than that, L = 12 + 3 = 15

your answer is **W = 12 units** and L = 15 units.

notice the patterns. you could use trial and error from the start. what 2 numbers that are 3 units apart multiply to 180. you can get it. but when they get harder or have decimals you'll find that the different algebra formulas and procedures are there to help.

Bets, Kim

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