SOLUTION: 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 sketc
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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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