The area of a rectangle is 432 square centimeters. what would the new area be if the length of the rectangle was decreased by $10\%$ and the width of the rectangle was increased by $10\%$? express your answer to the nearest whole number.

The correct question is
The area of a rectangle is 432 square centimeters. What would the new area be if the length of the rectangle was decreased by 10% and the width of the rectangle was increased by 10%? Express your answer to the nearest whole number.

let
x> the length of the rectangle
y> the width of the rectangle

we know that
area of rectangle=x*y
area of rectangle=432 cm²
so
432=x*y> equation 1

if the length of the rectangle was decreased by 10% and the width of the rectangle was increased by 10%
10% of x is 0.10x
10% of y is 0.10y
x1=x-0.10x---> 0.90x
y1=y+0.10x---> 1.10y

new area=(0.90x)*(1.10y)> 0.99*[x*y]
new area= 0.99*[x*y]> new area=0.99*[original area]
new area=0.99*432> 427.68 cm²
new area=428 cm²

the answer is
the new area is 428 cm²