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 = [tex]\frac{2}{3}[/tex]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 [tex]\frac{2}{3}[/tex]L
A = [tex]\frac{2}{3}[/tex][tex]L^{2}[/tex] ..................... 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 = [tex]\frac{2}{3}[/tex]L , then
A = (L + x ) X 1.25([tex]\frac{2}{3}[/tex]L)
A = (L + x ) X [tex]\frac{2.5L}{3}[/tex] ....................................... equation 2
Since we need to keep the Area the same , we will equate the two equations , this means that
[tex]\frac{2}{3}[/tex][tex]L^{2}[/tex] = (L + x ) X [tex]\frac{2.5L}{3}[/tex]
Which implies :
2[tex]L^{2}[/tex] = 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
