Question

The width of a rectangular room is $\frac{4}{7}$ of its length, $x$, and its perimeter is $y$. Write an equation connecting $x$ and $y$. Find the length of the room when the perimeter is $4400$ cm.

• A. $y=2x;2.2$ m
• B. $y=\frac{22}{7}x;14$ m
• C. $y=\frac{1}{7}x;28$ m
• D. $y=\frac{11}{7}x;28$ m

Answer 1

The correct option is B $y=\frac{22}{7}x;14$ m

Perimeter of the rectangle $=2(\frac{4}{7}x+x)$
$\Rightarrow y=2\left(\frac{4x+7x}{7}\right)$
$\Rightarrow y=\frac{22}{7}x$
If $y=4400$ cm
Then $4400=\frac{22x}{7}$
$\Rightarrow x=1400$ cm
$\Rightarrow x=14$ m