Question 64023This question is from textbook Algebra Structure and Method Book1
: A rectangle is three times as long as it is wide.If its length and width are both decreased by 2 cm,its area is decreased by 36 cm squared.Find its original dimensions.Make a sketch as in Oral Exercise 2.
This question is from textbook Algebra Structure and Method Book1
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! The area of a rectangle is given by:
In your rectangle: 
If you decrease the length, L, and the width, W, each by 2 cm, the area, A, is decreased by 36 sq.cm. So, puting this into an equation, you'll get:
 Substituting 3W for L, and L*W for A, you now have:
 Simplifying this, you'll get:
 Further simplification yields:
 and:
 Dividing by -8:
 and
so:
The original length, L = 15 cm
The original width, W = 5 cm
Check:
Original area:
After decreasing the lenth and width by 2 cm:
 sq.cm.
The decrease in area is:
 sq.cm.
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