The problem provides the width and length of a rectangle in terms of r, and its perimeter. We need to find…

Question

The problem provides the width and length of a rectangle in terms of r, and its perimeter. We need to find the values of the width and length.

ScanSolve AI Tutor · Accepted Answer

The problem provides the width and length of a rectangle in terms of $r$ , and its perimeter. We need to find the values of the width and length.

Given:
Width ( $w$ ) $= r$
Length ( $l$ ) $= 1.7320r$
Perimeter ( $P$ ) $= 14 + 10.3923$

Calculate the total perimeter.
First, sum the given parts of the perimeter.
$P = 14 + 10.3923$ $P = 24.3923$
Write the formula for the perimeter of a rectangle.
The formula for the perimeter of a rectangle is $P = 2(l + w)$ .
Substitute the given expressions for length and width into the perimeter formula.
Substitute $l = 1.7320r$ and $w = r$ into the perimeter formula, and set it equal to the calculated perimeter.
$24.3923 = 2(1.7320r + r)$
Solve the equation for $r$ .
Combine the terms inside the parenthesis and then solve for $r$ .
$24.3923 = 2(2.7320r)$ $24.3923 = 5.4640r$ $r = \frac{24.3923}{5.4640}$ $r \approx 4.4642$
Calculate the length and width.
Now substitute the value of $r$ back into the expressions for length and width.
Width:
$w = r$ $w = 4.4642$
Length:
$l = 1.7320r$ $l = 1.7320 \times 4.4642$ $l \approx 7.7320$
The width of the rectangle is approximately 4.4642 units and the length is approximately 7.7320 units.

The width is $\boxed{4.4642}$ and the length is $\boxed{7.7320}$ .

The problem provides the width and length of a rectangle in terms of r, and its perimeter. We need to find the values of the width and length.