The ratio of the width to the length of a rectangle is 2: 3, respectively. answer each of the following. b the width is increased by 25%. by what percent should the length change to keep the area the same?

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 =  ..................... 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

= (L + x ) X

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

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.