SOLUTION: After reducing by an equal amount the length and width of a rectangle which were originally 8cm and 5cm respectively.The area of the new rectangle is 18cm square.Find the dimension
Question 1208274: After reducing by an equal amount the length and width of a rectangle which were originally 8cm and 5cm respectively.The area of the new rectangle is 18cm square.Find the dimensions of the rectangle
First get some good mental exercise by solving the problem informally using logical reasoning and simple arithmetic.
The difference between the length and width of the original rectangle is 8-5 = 3cm. The length and width were reduced by the same amount, so the difference between the length and width of the new rectangle is still 3cm. The area of the new rectangle is 18 sq cm, so find two numbers whose difference is 3 and whose product is 18: 6 and 3. So the dimensions of the new rectangle are 6cm and 3cm.
Now solve the problem using formal algebra, which is probably what you are wanting to do.
Let x = # of cm by which the length and width were reduced.
The dimensions of the new rectangle are 8-x and 5-x; the area (length times width) is 18:
x = 11 or x = 2
Obviously x = 11 makes no sense in the given problem, so x is 2. So the dimensions of the new rectangle are
