A rectangle is three times as long as it is wide. If it’s length and width are both decreased by 2 cm, it’s area is decreased by 36 cm². Make a sketch and find its original dimensions.
in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

let L = the length and W = the width of the rectangle. According the problem we have L = 3W

so the area of the rectangle is A = 3W*W = 3W^2 cm^2

if we decrease the two dimentions of the rectangle by 2, we will have (L-2)(W-2) = 3W^2 -36

substituting on the first side where L = 3W the first side becomes;  (3W-2)(W-2) = 3W^2 - 6W - 2W + 4 -->>

3w^2 - 8W + 4 = 3W^2 - 36  --->>>  -8W = -40  --->>>  W = 5 cm and L = 15 cm ( because L=3W)

So the area is 3*5^2  = 3*25 = 75 cm^2  or 5*15 = 75 cm^2

check  (5-2)(15-2) = 3*13 = 39 and this is 36 less than 75
by Level 5 User (13.1k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,261 questions
86,786 answers
1,945 comments
3,648 users