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 W2 + 3W = 180 (by using the distributive property to multiply)
make it into a quadratic equation by subtracting 180 from both sides:
now we get W2 + 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.