the length of a rectangle is 16 cm greater than its width. the area is 35 m^2. find the dimension of the rectangle, to the nearest hundreth of a metre.

 ArcSine Posts: 948, Reputation: 518 Senior Member #2 Jul 22, 2012, 05:25 AM
Here you're given two facts about the situation, which can be expressed as

L = W + 16

L • W = 350,000

...where L and W represent the rectangle's length and width, respectively. (Since L and W are given in terms of cm, we're putting the rectangle's area into the same terms, recognizing that 1 m^2 = 10,000 cm^2.)

Since the first one says that "W + 16" is just another way of saying "L", we can use this fact as a substitution in the second one, so that the second one becomes an equation in just one variable

(W + 16) • W = 350,000

From here, expand out the left-hand side, then deduct 350K from both sides to produce a quadratic equation in standard form. Then, as with your baseball-distance question, use the quadratic formula to determine W.

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