SOLUTION: A rectangular picture frame measures 30cm by 40cm. A new frame is to be made by increasing each side length by the same amount. The resulting enclosed area is to be 1656cm^2.Find t

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Question 937042: A rectangular picture frame measures 30cm by 40cm. A new frame is to be made by increasing each side length by the same amount. The resulting enclosed area is to be 1656cm^2.Find the dimensions of the new picture frame.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular picture frame measures w cm by L cm. A new frame is to be made by increasing each side length by the same amount, u. The resulting enclosed area is to be T cm^2.Find the dimensions of the new picture frame, meaning w+u and L+u.

Notice this is not the same as a "uniform border" type of rectangle area problem.

Original area, wL.
New area, (w+u)(L+u)
New area also given, T
UNKNOWN is u.

highlight%28%28w%2Bu%29%28L%2Bu%29=T%29
Quadratic equation in the unknown variable, u.
You can solve this purely symbolically first, or you can substitute the given values any time and solve that way.