Answer:
New width will be [tex]6.807\ ft[/tex] larger than old width.
Step-by-step explanation:
Given width of room is [tex]9.3\ ft[/tex]
And length of room is [tex]6.2\ ft[/tex]
Then the old area will be [tex](9.3\times 6.2)[/tex]
Also we have to make this room three times larger as it is now.
We can see the ratio between width and length of room is [tex]\frac{9.3}{6.2}=1.5[/tex]
let us say the length of new room is [tex]x[/tex]
So, width of room will be [tex]1.5\times x[/tex]
And we know area of rectangle is [tex]length\times width[/tex]
Also, the new area will be [tex]3\times (9.3\times 6.2)[/tex]
Then the equation will be
[tex]x\times 1.5\times x=3\times(9.3\times 6.2)\\1.5\times x^2=172.89\\x^2=\frac{172.89}{1.5}\\ x^2=115.32\\x=\sqrt{115.32}\\x=10.73\ ft[/tex]
So, the width of new room is
[tex]1.5\times x=1.5\times 10.738\\width=16.107\ ft[/tex]
So, the increment in width is
[tex]16.107-9.3=6.807\ ft[/tex]
