Solved: "A wire of length r feet is bent..."

High School
Geometry
High school geometry
Solid Geometry

ringearV

Answered question

2021-05-09

A wire of length r feet is bent into a rectangle whose width is 2 times its height. Write the area A of the rectangle as a function of the wires

Answer & Explanation

wornoutwomanC

Skilled2021-05-10Added 81 answers

The length of the wire is the perimeter of the rectangle with width ww and height hh:
$2 w + 2 h = r$
Given that the width is 2 times its height, $w = 2 h$ , we write: $2 (2 h) + 2 h = r$
$4 h + 2 h = r$
$6 h = r$
$h = \frac{r}{6}$
which follows that:
$w = 2 \cdot \frac{r}{6} = \frac{r}{3}$
The area of the rectangle is:
$A = w h$
In terms of r,
$A = r 3 \cdot r 6$
$A = \frac{r^{2}}{18}$
Solve for rr in terms of AA:
$18 A = r^{2}$
$\sqrt{18 A} = r$
or
$r = 3 \sqrt{2 A}$

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

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