Gọi cd, cr là a,b(cm)(a,b∈N*)
\(a:b=4:7\Leftrightarrow\dfrac{a}{4}=\dfrac{b}{7}\)
Đặt \(\dfrac{a}{4}=\dfrac{b}{7}=k>0\Leftrightarrow a=4k;b=7k\)
Ta có \(ab=112\Leftrightarrow28k^2=112\Leftrightarrow k^2=4\Leftrightarrow k=2\left(k>0\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=8\\b=14\end{matrix}\right.\)
Vậy chu vi là \(\left(a+b\right)\cdot2=44\left(cm\right)\)