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 Nov 6, 2016
edited by Guest  Nov 6, 2016
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An area of a rectangle is 322cm^2. One side is 9 cm longer than the other. Find the dimensions.

 

Area = Width x Length

Let Width = W, then:

The Length=W + 9

 

322 =W x [W + 9], solve for W

Solve for W:
322 = W (W+9)

322 = W (W+9) is equivalent to W (W+9) = 322:
W (W+9) = 322

Expand out terms of the left hand side:
W^2+9 W = 322

Add 81/4 to both sides:
W^2+9 W+81/4 = 1369/4

Write the left hand side as a square:
(W+9/2)^2 = 1369/4

Take the square root of both sides:
W+9/2 = 37/2 or W+9/2 = -37/2

Subtract 9/2 from both sides:
W = 14 or W+9/2 = -37/2

Subtract 9/2 from both sides:
Answer: |W = 14                   or                 W = -23 (Discard this one)

 

Then the Width =14 cm    and the Length=14 + 9 =23 cm

 Nov 6, 2016

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