Calculation:

Since, the side of the triangle \(\displaystyle\triangle{A}{B}{C}\) is 75% of the side of the triangle \(\displaystyle\triangle{D}{E}{F}\).

\(\displaystyle\frac{{{A}{B}}}{{{D}{E}}}=\frac{{{75}}}{{{100}}}\)

\(\displaystyle{A}{B}=\frac{{3}}{{4}}{D}{E}\)...(1)

and, the side of the triangle \(\displaystyle\triangle{G}{H}{I}\) is 32% of the side of the triangle \(\displaystyle\triangle{D}{E}{F}\).

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{32}}}{{{100}}}\)

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{8}}}{{{25}}}\)

\(\displaystyle{D}{E}=\frac{{{25}}}{{{8}}}{G}{H}\)...(2)

Substitute equation (1) in equation (2).

\(\displaystyle{A}{B}=\frac{{3}}{{4}}{\left(\frac{{{25}}}{{{8}}}{G}{H}\right)}\)

\(\displaystyle\frac{{{A}{B}}}{{{G}{H}}}=\frac{{{75}}}{{{32}}}\)

Therefore, the ratio of the sides of the triangles ABC and GHI is \(\displaystyle\frac{{{75}}}{{{32}}}\).

Since, the side of the triangle \(\displaystyle\triangle{A}{B}{C}\) is 75% of the side of the triangle \(\displaystyle\triangle{D}{E}{F}\).

\(\displaystyle\frac{{{A}{B}}}{{{D}{E}}}=\frac{{{75}}}{{{100}}}\)

\(\displaystyle{A}{B}=\frac{{3}}{{4}}{D}{E}\)...(1)

and, the side of the triangle \(\displaystyle\triangle{G}{H}{I}\) is 32% of the side of the triangle \(\displaystyle\triangle{D}{E}{F}\).

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{32}}}{{{100}}}\)

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{8}}}{{{25}}}\)

\(\displaystyle{D}{E}=\frac{{{25}}}{{{8}}}{G}{H}\)...(2)

Substitute equation (1) in equation (2).

\(\displaystyle{A}{B}=\frac{{3}}{{4}}{\left(\frac{{{25}}}{{{8}}}{G}{H}\right)}\)

\(\displaystyle\frac{{{A}{B}}}{{{G}{H}}}=\frac{{{75}}}{{{32}}}\)

Therefore, the ratio of the sides of the triangles ABC and GHI is \(\displaystyle\frac{{{75}}}{{{32}}}\).