SOLUTION: the perimeter of a rectangle is 26cm.The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.Find the dimension of the original

Question 850106: the perimeter of a rectangle is 26cm.The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.Find the dimension of the original rectangle
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the perimeter of a rectangle is 26cm. The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.
Find the dimension of the original rectangle
:
2L + 2W = 26
simplify, divide by 2
L + W = 13
L = (13-W); use this form for substitution
Area = LW
and
New area = old area
(L-3)*(W+2) = LW
Foil
LW + 2L - 3W - 6 = LW
Subtract LW from both sides
2L - 3W + 6 = 0
Replace L with (13-W)
2(13-W) - 3w - 6 = 0
26 - 2W - 3W - 6 = 0
-5W + 20 = 0
-5W = -20
W = -20/-5
W = 4 cm is the original Width
then
13 - 4 = 9 cm is the length
:
You can check the area of each, ensure they are equal

RELATED QUESTIONS
The length of a rectangle is 3cm longer than its width. If the perimeter of the... (answered by mananth)

the perimeter of a rectangle is 240cm . if the lenght is decreased .if the lenght is... (answered by ankor@dixie-net.com)

the length of rectangle is increased by 2 cm. if length is increased by 4cm and breadth... (answered by CharlesG2)

the perimeter of a rectangle is 26 centimeters. the area of the rectangle remains the... (answered by Theo)

If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased... (answered by josgarithmetic)

If the area of a rectangle is 30cm and the perimeter is 26cm. What is the length and... (answered by josgarithmetic)

If lenght of a rectangle is increased by 30% and the width is decreased by 20% then by... (answered by KMST)

If AD=(x+6)cm, AB=5cm and the perimeter of ABCD is 26cm, find the area of rectangle... (answered by checkley77)

The length of a rectangle is 8cm longer than the width. If the width is increased by 4cm... (answered by ikleyn)