# SOLUTION: A rectangle is three times as long as it is wide. If the length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions. Make a sketch a

Algebra ->  -> SOLUTION: A rectangle is three times as long as it is wide. If the length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions. Make a sketch a      Log On

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 Question 176099This question is from textbook : A rectangle is three times as long as it is wide. If the length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions. Make a sketch as in oral exercise 2.This question is from textbook Answer by EMStelley(187)   (Show Source): You can put this solution on YOUR website!Let's call the width of the rectangle w. Then the length can be represented by 3w since the "rectangle is three times as long as it is wide." The next statement, "if the length and width are both decreased by 2 cm", can be written as a width of w-2 and a length of 3w-2. Now, the area of the rectangle is w*3w, so if the "area is decreased by 36 cm^2", this is written as 3w^2-36. So, our equation to solve is: We need to solve for w, so first, let's multiply out the left hand side: Now, combine like terms on the left hand side: Now, subtract 3w^2 from both sides: Subtract 4 from both sides: Divide both sides by -8: So the width of the rectangle is 5 cm, meaning that the length is 5(3)=15 cm. I will leave the drawing up to you.