Question

What is the width of the rectangle?

Area: 24 3/4
Length: 6 1/2
Width:

Answer 1

let's firstly convert the mixed fractions to improper fractions.

`\bf \stackrel{mixed}{24(3)/(4)}\implies \cfrac{24\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{99}{4}}~\hfill \stackrel{mixed}{6(1)/(2)}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \stackrel{\textit{area of a rectangle}}{A=Lw}\implies \cfrac{A}{L}=w~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=(13)/(2)\\\\ A=(99)/(4) \end{cases}\implies \cfrac{~~(99)/(4)~~}{(13)/(2)}=w \\\\\\ \cfrac{99}{4}\cdot \cfrac{2}{13}=w\implies \cfrac{99}{13}\cdot \cfrac{2}{4}=w\implies \cfrac{99}{13}\cdot \cfrac{1}{2}=w\implies \cfrac{99}{26}=w\implies 3(21)/(26)=w`