Question

The diagram shows the outline of a room. The owner has decided to make the room three times as large as it is now. How many feet wide will the new room be?

Answer 1

Answer:

New width will be $6.807\ ft$ larger than old width.

Step-by-step explanation:

Given width of room is $9.3\ ft$

And length of room is $6.2\ ft$

Then the old area will be $(9.3\times 6.2)$

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 $\frac{9.3}{6.2}=1.5$

let us say the length of new room is $x$

So, width of room will be $1.5\times x$

And we know area of rectangle is $length\times width$

Also, the new area will be $3\times (9.3\times 6.2)$

Then the equation will be

$x\times 1.5\times x=3\times(9.3\times 6.2)\\1.5\times x^2=172.89\\x^2=\frac{172.89}{1.5}\\ x^2=115.32\\x=\sqrt{115.32}\\x=10.73\ ft$

So, the width of new room is

$1.5\times x=1.5\times 10.738\\width=16.107\ ft$

So, the increment in width is

$16.107-9.3=6.807\ ft$