SOLUTION: The combined area of a square and a rectangle is 201 square centimeters. The width of the rectangle is 5 centimeters more than the length of a side of the square, and the length of

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Question 963586: The combined area of a square and a rectangle is 201 square centimeters. The width of the rectangle is 5 centimeters more than the length of a side of the square, and the length of the rectangle is 4 centimeters more than its width. Find the dimensions of the square and the rectangle.
Answer by macston(5194) About Me  (Show Source):
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s=Side of square; W=width of rectangle=s+5cm; L=length of rectangle=W+4cm=s+9cm
Area of square=s^2; Area of rectangle=(L)(W)
Total Area=area of square + area of rectangle
201cm%5E2=s%5E2%2B%28L%29%28W%29
201cm%5E2=s%5E2%2B%28s%2B9cm%29%28s%2B5cm%29
201cm%5E2=s%5E2%2Bs%5E2%2B14s%2B45%29
0=2s%5E2%2B14s-156
0=s%5E2%2B7s-78
0=%28s%2B13%29%28s-6%29
s%2B13=0 or s-6=0
s=-13 or s=6
ANSWER 1: The sides of the square are 6 cm
W=s%2B5cm=6cm%2B5cm=11cm ANSWER 2: The width of the rectangle is 11 cm.
L=W%2B4cm=11cm%2B4cm=15cm ANSWER 3: The length of the rectangle is 15 cm.
CHECK:
Total Area = area of square + area of rectangle
201cm%5E2=s%5E2%2B%28L%29%28W%29
201cm%5E2=%286cm%29%5E2%2B%2811cm%29%2815cm%29
201cm%5E2=36cm%5E2%2B165cm%5E2
201cm%5E2=201cm%5E2