SOLUTION: The length of a rectangle is greater than its breadth by 2 cm. If the length is increased by 4 cm and the breadth decreased by 3 cm, the area remains the same. Find the length and

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is greater than its breadth by 2 cm. If the length is increased by 4 cm and the breadth decreased by 3 cm, the area remains the same. Find the length and       Log On


   

Question 955329: The length of a rectangle is greater than its breadth by 2 cm. If the length is increased by 4 cm and the breadth decreased by 3 cm, the area remains the same. Find the length and breadth of the rectangle.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=breadth; L=length=W+2cm
W*L=(L+4cm)(W-3cm) Substitute for L.
W(W+2cm)=(W+2cm+4cm)(w-3cm)
W%5E2%2B2Wcm=%28W%2B6cm%29%28W-3cm%29
W%5E2%2B2Wcm=W%5E2%2B3Wcm-18cm%5E2 Subtract W^2 from each side.
2Wcm=3Wcm-18cm%5E2 Subtract 2Wcm from each side.
0=Wcm-18cm%5E2 Add 18cm^2 to each side.
18cm%5E2=Wcm Divide each side by 1cm.
18cm=W ANSWER 1: The width is 18 centimeters.
L=W+2cm=18cm+2cm=20cm ANSWER 2: The length is 20 centimeters.
CHECK:
W*L=(L+4cm)(W-3cm)
%2820cm%29%2818cm%29=%2824cm%29%2815cm%29
360cm%5E2=360cm%5E2