Math CentralQuandaries & Queries


Question from Bali, a student:

if the length of the rectangular field is decreased by 5m,its area is decreased by 70 sqm. if the width is increased by 6m, the area is increased by 180 sqm. determine the length and width of the rectangular field?


If a rectangle is L metres in length and W metres in width then its area is $L \times W$ square metres.

Suppose your original rectangle is x metres long and y metres wide. What is its area?

Suppose you decrease the length by 5 meters, what is its length now? What is the area of this modified rectangle? This area is 70 square metres less than the original area. Write this as an equation.

Apply the same procedure when you decrease the width of the original rectangle by 6 metres. This will give you a second equation. Solve the equations for x and y.


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