Answer: a) The percent of change in perimeter is 100%.
b) The percent of change in area is 300%.
Step-by-step explanation:
Since we have given that
if the side lengths of rectangle get doubled.
Let the length be 'x'.
Let the breadth be 'y'.
So, Perimeter of rectangle would be
[tex]2(x+y)[/tex]
Area of rectangle would be
[tex]xy[/tex]
After doubling the lengths,
Length becomes '2x'.
Width becomes '2y'.
So, perimeter becomes
[tex]2(2x+2y)\\\\=4(x+y)[/tex]
Area becomes
[tex]2x\times 2y\\\\=4xy[/tex]
a. Find the percent of change in the perimeter.
[tex]\dfrac{4(x+y)-2(x+y)}{2(x+y)}\times 100\\\\=\dfrac{2(x+y)}{2(x+y)}\times 100\\\\=100\%[/tex]
Hence, the percent of change in perimeter is 100%.
b. Find the percent of change in the area.
[tex]\dfrac{4xy-xy}{xy}\times 100\\\\=\dfrac{3xy}{xy}\times 100\\\\=300\%[/tex]
Hence, the percent of change in area is 300%.
