Answer:
Part a) [tex]A=\frac{3}{4}L^2\ units^2[/tex]
Part b) The width of the rectangle is now 37.5% of its length or is now half of 75% of its length.
Step-by-step explanation:
Part a) What is the area of the rectangle?
Let
L ----> the length of rectangle
W ---> the width of the rectangle
Remember that
[tex]75\%=\frac{75}{100}=\frac{3}{4}[/tex]
we know that
The area of rectangle is
[tex]A=LW[/tex] ----> equation A
we have
[tex]W=\frac{3}{4}L[/tex] -----> equation B
substitute equation B in equation A
[tex]A=L(\frac{3}{4}L)[/tex]
[tex]A=\frac{3}{4}L^2\ units^2[/tex]
Part b) The length of the rectangle is doubled. What percent of the length is the width now?
we know that
The length is now 2L (represent the 100%)
The width is 0.75L
using proportion
Find out what percent of the length is the width now
[tex]\frac{2L}{100\%}=\frac{0.75L}{x}\\\\x=0.75L(100)/2L\\\\x=37.5\%[/tex]
therefore
The width of the rectangle is now 37.5% of its length or is now half of 75% of its length.
