Answer: The length should be reduced by 20%
Step-by-step explanation:
The ratio of the width to the length of a rectangle is 2:3, respectively , this means that
W =
L
Area of rectangle is given as Length x width , this means
A = L X W
Substituting into the Area , we have
A = L x
L
A = ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
..................... equation 1
Width is increased by 25 % , so new width = 1.25W
Let the increase in Length be x , then new Length = L + x
Area = Length x Width
A = (L+x) X 1.25W
Recall that W =
L , then
A = (L + x ) X 1.25(
L)
A = (L + x ) X
....................................... equation 2
Since we need to keep the Area the same , we will equate the two equations , this means that
![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
= (L + x ) X ![\frac{2.5L}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2.5L%7D%7B3%7D)
Which implies :
2
= 2.5L(L + x )
divide through by 2.5L
0.8L = L + x
Therefore :
x = 0.8L - L
x = - 0.2 L
Since x represents the change in L and it gives negative , this means that the Length should be reduced by 20% to keep the area the same