Respuesta :
Answer:
By 20% the width of tapestry was decreased in the process.
Step-by-step explanation:
Given : A designer increased the area of a tapestry by 20% and length was increased by 50%?
To find : By what percent the width of tapestry was decreased in the process?
Solution : Let the length and width of the tapestry is l and w respectively.
So, The area of tapestry is [tex]A=l\times w[/tex]
According to question,
A designer increased the area of a tapestry by 20%.
i.e, The new area is [tex]A_N= lw+20\% ( lw)[/tex]
[tex]A_N= lw+\frac{1}{5} (lw)=\frac{6}{5}lw[/tex]
And length was increased by 50%
i.e, The new length is [tex]l= l+50\% l[/tex]
[tex]l= l+\frac{1}{2}l=\frac{3}{2}l[/tex]
and let the new width is w'
Then the area is [tex]A=\frac{3}{2}lw'[/tex]
So, to find the new width is
Area = New area
[tex]\frac{3}{2}lw'=\frac{6}{5}lw[/tex]
[tex]w'=\frac{12}{15}w[/tex]
The percentage of width of tapestry decreased is
[tex]\% change= (1-w')\times 100[/tex]
[tex]\% change= (1-\frac{12}{15}w)\times 100[/tex]
[tex]\% change=\frac{3}{15}w\times 100[/tex]
[tex]\% change=20\%w[/tex]
Therefore, By 20% the width of tapestry was decreased in the process.
