Question

the length of the rectangle is increased by 50% by what percent should the width be decreased to maintain the same area​

Answer 1

it will decrease by 25 %

Answer 2

Since the formula for the area of a rectangle is A=L⋅BA=L⋅B, increasing one dimension by a factor of k will increase the area by a factor of k— unless the other dimension is multiplied by 1k1k:

A=L⋅B=(L⋅k)(B⋅1k)A=L⋅B=(L⋅k)(B⋅1k)

Increasing L by 50% means multiplying by k=1.50=32k=1.50=32; to maintain the same area, Bmust be multiplied by 1k=11.5=(32)−1=23=0.6¯¯¯1k=11.5=(32)−1=23=0.6¯

(L⋅32)(B⋅23)=L⋅B(32⋅23)=L⋅B=A(L⋅32)(B⋅23)=L⋅B(32⋅23)=L⋅B=A

Multiplying B by 2323 or 0.6¯¯¯0.6¯ means decreasing Bby 1313 or 0.3¯¯¯0.3¯, or about 33.3%.