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
