# The length of the rectangle was reduced by a third of the width by a quarter by which

The length of the rectangle was reduced by a third of the width by a quarter by which part the area of the rectangle was reduced.

1. Since the length and width of the rectangle are not known to us, we denote the value of the length A, and the value of the width will be B.

2. Initially, the area of this rectangle was (A x B).

3. The length of the rectangle has been reduced by a third and now it is equal to:

A – (1/3) A = (2/3) A.

4. The width was reduced by a quarter, the width became:

B – (1/4) B = (3/4) B.

5. The area of the new rectangle is:

(2/3) A x (3/4) B = (2/3) x (3/4) x (A x B) = (2 x 3) / (3 x 4) x (A x B) = (6/12) (A x B) =

= (1/2) (A x B).

This means that the area of the rectangle has decreased by 1/2.

Answer: the area of the rectangle has been reduced by 1/2.

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