SOLUTION: hi, im in algebra 1 and i dont understand how to do the math word problems. Their the ones tht are like if u have a rectangle with an area of 190 square feet, what is the length i

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: hi, im in algebra 1 and i dont understand how to do the math word problems. Their the ones tht are like if u have a rectangle with an area of 190 square feet, what is the length i      Log On


   

Question 285483: hi, im in algebra 1 and i dont understand how to do the math word problems. Their the ones tht are like if u have a rectangle with an area of 190 square feet, what is the length if the width is 2 units less than the length.
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
This problem would be solved as follows:

L = length
W = width

Since the width is 2 less than the length, this means that:

W = L - 2

Now the area of the rectangle is equal to 190 square feet.

Area of a rectangle is length * width.

This means the formula is:

L * W = 190

Since you know that the width is 2 less than the width, you get the formula of:

W = L - 2 that we showed above.

You can substitute L - 2 in the equation of L * W = 190 to get:

L * W = 190 becomes:

L * (L-2) = 190

Now you have 1 equation in 1 unknown (L) which you can solve.

L * (L-2) = 190 becomes:

L^2 - 2*L = 190 once you make the replacement.

Subtract 190 from both sides of this equation to get:

L^2 - 2*L - 190 = 0

This is a quadratic equation that you can solve by factoring or by use of the quadratic formula.

The standard form of a quadratic equation is:

ax^2 + bx + c = 0

The standard form of your equation is:

aL^2 + bL + c = 0 since you are using L instead of x.

In your equation:

a = 1
b = -2
c = -190

You plug these values into the quadratic formula of:

L = (-b +/- sqrt(b^2-4ac))/(2a)

to get the roots.

The roots become:

L = 14.82027496 or L = -12.82027496

I checked those roots out by plugging into the original equation and they are good.

L can't be negative, so L has to be 14.82027496

Go back to your original equation to see if this values satisfies it.

You have your original formula of L*W = 190

You also have that W = L - 2

If L is equal to 14.82027496, then W = L - 2 is equal to 12.82027496.

L * W = 190 becomes:

14.82027496 * 12.82027496 = 190 confirming that these values are good.















Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

Almost no one in algebra understands the word problems.
Just curious.
Had you looked for similar problems before posting?
Had you looked for lessons before posting?