SOLUTION: the width of a rectangle is 40 cm less than its perimeter. The rectangle's are is 102 square cm. find the dementions

Question 946751: the width of a rectangle is 40 cm less than its perimeter. The rectangle's are is 102 square cm. find the dementions
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
ASSIGN VARIABLES
w, width of rectangle
L, length of rectangle
p, perimeter of rectangle
A, area of rectangle
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A=102
w=p-40
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UNKNOWNS: w and L.

Note that although p is unknown, it can be eliminated using the w equation
and the p equation.

-
Equate the two expressions for p;

Simplify

The simpler equivalent system without p is

Substitute for w in the area A equation:

simplify

Substituting the given value now for A would be convenient.

FACTORABLE.

-
EITHER OR .

Find width, w, using the earlier found formula from the process,
w=40-2L:
EITHER OR

SUMMARY OF SOLUTIONS
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The dimensions are either 3 & 34, or 17 & 6.
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