Answer:
The length of cuboid is [tex]\sf{7\dfrac{1}{5} \: in}[/tex]
Step-by-step explanation:
Here's the required formula to find the length of cuboid :
[tex]\longrightarrow{\pmb{\sf{V = \ell \times w \times h}}}[/tex]
- [tex]\pink\star[/tex] V = Volume
- [tex]\pink\star[/tex] l = length
- [tex]\pink\star[/tex] w = width
- [tex]\pink\star[/tex] h = height
Substituting all the given values in the formula to find the length of cuboid :
- [tex]\purple\star[/tex] V = 60
- [tex]\purple\star[/tex] l = ?
- [tex]\purple\star[/tex] w = 2½
- [tex]\purple\star[/tex] h = 3⅓
[tex]\implies{\sf{V = \ell \times w \times h}}[/tex]
[tex]\implies{\sf{60= \ell\times 2\dfrac{1}{2} \times 3\dfrac{1}{3}}}[/tex]
[tex]\implies{\sf{60= \ell\times \dfrac{4 + 1}{2} \times \dfrac{9 + 1}{3}}}[/tex]
[tex]\implies{\sf{60= \ell\times \dfrac{5}{2} \times \dfrac{10}{3}}}[/tex]
[tex]\implies{\sf{60= \ell\times \dfrac{5 \times 10}{2 \times 3}}}[/tex]
[tex]\implies{\sf{60= \ell\times \dfrac{50}{6}}}[/tex]
[tex]\implies{\sf{\ell = 60 \times \dfrac{6}{50}}}[/tex]
[tex]\implies{\sf{\ell = \dfrac{60 \times 6}{50}}}[/tex]
[tex]\implies{\sf{\ell = \dfrac{360}{50}}}[/tex]
[tex]\implies{\sf{\ell = \dfrac{36 \cancel{0}}{5 \cancel{0}}}}[/tex]
[tex]\implies{\sf{\ell = \dfrac{36}{5}}}[/tex]
[tex]\implies{\sf{\ell = 7\dfrac{1}{5}}}[/tex]
[tex]\star{\underline{\boxed{\tt{\red{\ell = 7\dfrac{1}{5} \: in}}}}}[/tex]
Hence, the length of cuboid is 7(1/5) in.
[tex]\rule{300}{2.5}[/tex]
