A rectangle is twice as long as it is wide. If its length and widtb are both decreased by 4cm, its area is decreased by 164cm^2. Find its original dimensions

Question

its decreased by 4cm then its goes down 164cm^2

Answer 1

Let's start with the basic equation of the area of a rectangle A=l*w

If the rectangle is twice as long as it is wide then we know l=2*w

Substituting this into the original equation, we can write the original area before any modification as A=2w*w or A=2w²

Modifying the previous equation, if we decrease the original length and width both by 4 and the original area by 164, we are left with A-164=(2w-4)(w-4)

Because we know the original area A is defined as A=2w², we can substitute this into the new equation, giving us 2w²-164=(2w-4)(w-4)

Solve for w

2w²-164=(2w-4)(w-4)

2w²-164=2w²-8w-4w+16

-12w=-180

w=15

The original width was 15 cm and the length was 30 cm.