# Thread: Area reduction problem

1. ## Area reduction problem

I have a rectangle which consists of a width of 10", and a length of 40". THis gives me a total area of 400" (w x l= a). If I reduce the area by a percentage, lets say 10% my reduced area is now 360" (400 - 40 = 360.) What is the formula to determine the reduced size of the width and the length.

W = 10"
L = 40"
A = 400

reduced rectangle 10% of area
A2 = 360
W2 = ?
L2 = ?

Thanks for your help.

2. Originally Posted by ronheid
I have a rectangle which consists of a width of 10", and a length of 40". THis gives me a total area of 400" (w x l= a). If I reduce the area by a percentage, lets say 10% my reduced area is now 360" (400 - 40 = 360.) What is the formula to determine the reduced size of the width and the length.

W = 10"
L = 40"
A = 400

reduced rectangle 10% of area
A2 = 360
W2 = ?
L2 = ?

Thanks for your help.
Reduce both width and length by 5.13% (leaving 94.87%). Since $0.9487 \cdot 0.9487 \approx 0.90$, this will reduce the area by 10%.

The general formula: To reduce the area by x%, reduce the linear dimensions by $100\left(1 - \sqrt{1 - \frac{x}{100}}\right)\%$.