SOLUTION: if the Area of a rectangle is 105 sq. in., and the Perimeter is 44 in., what would be the measurement of its' length and width? This is what I've done so far; A=1w (105 sq.

Algebra ->  Trigonometry-basics -> SOLUTION: if the Area of a rectangle is 105 sq. in., and the Perimeter is 44 in., what would be the measurement of its' length and width? This is what I've done so far; A=1w (105 sq.      Log On


   

Question 834921: if the Area of a rectangle is 105 sq. in., and the Perimeter is 44 in., what would be the measurement of its' length and width?
This is what I've done so far; A=1w (105 sq. in)
P=2(1+w) = 44
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
That is a good start. CONTINUE!

Let's use L for length instead of the lower case "l", because it looks like a variable and not a digit.

You know area A and you know perimeter P.
You want to know length L and width w.

Equations for the system are as you saw, 2%28L%2Bw%29=P and Lw=A.

Solve for one unknown from one equation and substitute the formula into the other equation! That is what is meant by, "CONTINUE!". I will keep this generalized, really not caring about the actual values of P and A.

2L%2B2w=P
2L=P-2w
L=%28P-2w%29%2F2
-
Lw=A
%28%28P-2w%29%2F2%29w=A
%28P-2w%29w=2A
Pw-2w%5E2=2A
-2w%5E2-2A%2BPw=0
-2w%5E2%2BPw-2A=0
2w%5E2-Pw%2B2A=0 --------- If the values for A and P make this factorable, then you can solve that way. Otherwise, use the general solution for a quadratic equation:
highlight%28w=%28P%2B-+sqrt%28P%5E2-4%2A%282%29%2A%282A%29%29%29%2F%282%2A2%29%29
And find L from knowing value of w.