what is the original length and width of the rectangle

Question

the perimeter of a rectangle is 62 meters if the width were doubled and the length were increased by 21 meters the perimeter would be 120 meters

Answer 1

We define variables.

   x : the width of original rectangle

   y : the height of original rectangle

The first statement is written as an equation, based on the formula for rectangular perimeter.

   62 = 2x + 2y

The other statement is a bit trickier.

   120 = 2(2x) + 2(y+21)

But now we have a system of two equations (and two unknowns). We simplify the equations by dividing by 2.

   31 = x + y

   60 = 2x + y + 21

We use elimination: we subtract the equations (first from second).

   29 = x + 21

We subtract 21 from both sides.

   8 = x

We substitute 8 for x in an equation that also has y.

   31 = 8 + y

We subtract 8 from both sides.

   23 = y

Thus, the original dimensions were 8 meters wide by 23 meters long. This should be checked.