SOLUTION: The length of a rectangle is 3 centimeters more than its width. If the width is increased by 5 centimeters and the length is increased by 7 centimeters, a new rectangle is formed t

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 3 centimeters more than its width. If the width is increased by 5 centimeters and the length is increased by 7 centimeters, a new rectangle is formed t      Log On


   

Question 940652: The length of a rectangle is 3 centimeters more than its width. If the width is increased by 5 centimeters and the length is increased by 7 centimeters, a new rectangle is formed that has an area of 134 square centimeters more than the area of the original rectangle. Find the dimensions of the original rectangle.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Width=W, Length=W+3, New Width=W+5, New Length=W+10
Original area=W(W+3)=W%5E2%2B3W
New area=(W+5)(W+10)=W%5E2%2B15W%2B50
Difference in area=%28W%5E2%2B15W%2B50%29-%28W%5E2%2B3W%29=W%5E2%2B15W%2B50-W%5E2-3W=
12W+50=134 cm
Solve for W:
12W=84 cm
W=7 cm ANSWER 1 Original Width
L=W+3 cm=7 cm+ 3 cm=10 cm ANSWER 2 Original Length
New W=W+5 cm=7 cm + 5 cm=12 cm; New L=L+7 cm=10 cm + 7cm=17
Old Area=L%2AW=10+cm%2A+7+cm=70+cm%5E2
New Area =New+L%2ANew+W=17+cm+%2A+12+cm=204+cm%5E2
CHECK:
Difference in Area = 134+cm%5E2
Difference in Area=New Area-Old Area=134cm%5E2
Difference in Area=204+cm%5E2+-+70+cm%5E2=134+cm%5E2=134+cm%5E2