SOLUTION: The perimeter of a rectangle is 70 cm the length of the rectangle is 5 cm more than four times the width. find the length and the width of the rectangle.

Algebra ->  Average -> SOLUTION: The perimeter of a rectangle is 70 cm the length of the rectangle is 5 cm more than four times the width. find the length and the width of the rectangle.      Log On


   

Question 863919: The perimeter of a rectangle is 70 cm the length of the rectangle is 5 cm more than four times the width. find the length and the width of the rectangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be length and y be width.
Let p be perimeter.
Formula for perimeter is 2%28x%2By%29=p.
Your description can be generalized into, "perimeter of a rectangle is p cm. The length,x, of the rectangle is n cm more than m times the width of y."

The description like that symbolically is ... x=n%2Bmy.
KNOWN: p, m, n.
UNKNOWN: x, y.

EQUATIONS FOR A SYSTEM:
2%28x%2By%29=p and x=n%2Bmy.
Substitute for x.
2%28n%2Bmy%2By%29=p
2n%2B2my%2B2y=p
2my%2B2y=p-2n
y%282m%2B2%29=p-2n
highlight%28y=%28p-2n%29%2F%282m%2B2%29%29. This is one of the dimensions answered.
-
Use the description translated about x to find the symbolic form for x.
x=n%2Bmy---From the translation.
highlight%28x=n%2Bm%28%28p-2n%29%2F%282m%2B2%29%29%29. The other dimension answered.
You can stop right there, or you can continue putting into a fully rational form...
x=n%282m%2B2%29%2F%282m%2B2%29%2Bm%28p-2n%29%2F%282m%2B2%29
x=%282mn%2B2n%2Bmp-2np%29%2F%282m%2B2%29. This form for the other dimension if you want it this way.

Recall the values given for p, m, and n.