To determine: The ratio of the sides of the triangles ABC and GHI. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

To determine: The ratio of the sides of the triangles ABC and GHI. Given: Triangle ABC that is 75% of its corresponding side in triangle DEF. Triangle GHI that is 32% of its corresponding side in triangle DEF.

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asked 2021-03-09
To determine: The ratio of the sides of the triangles ABC and GHI.
Given:
Triangle ABC that is 75% of its corresponding side in triangle DEF.
Triangle GHI that is 32% of its corresponding side in triangle DEF.

Answers (1)

2021-03-10
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 \(\displaystyle\frac{{{75}}}{{{32}}}\).
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