Step 1

Given two triangles are :

Step 2

\(\displaystyle\triangle{G}{H}{I}\),

GH=42, HI=17, IG=48

\(\displaystyle\triangle{L}{M}{N}\),

LM=21, MN=10, NL=30

Step 3

We know that if two triangles are similar then their sides are in equal ratio.

if \(\displaystyle\triangle{G}{H}{I}\ {\quad\text{and}\quad}\ \triangle{L}{M}{N}\) are similar then,

\(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{G}{I}}}{{{L}{N}}}}\)

Here,

\(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{42}}}{{{21}}}}={2}\)

\(\displaystyle{\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{17}}}{{{10}}}}={1.7}\)

\(\displaystyle{\frac{{{G}{I}}}{{{L}{N}}}}={\frac{{{48}}}{{{30}}}}={1.6}\),

That means, \(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}\ne{q}{\frac{{{H}{I}}}{{{M}{N}}}}\ne{q}{\frac{{{G}{I}}}{{{L}{N}}}}\)

Hence given two triangles are not similar, \(\displaystyle\triangle{G}{H}{I}{n}\sim\triangle{L}{M}{N}\)

Answer : These triangles are not similar.

Given two triangles are :

Step 2

\(\displaystyle\triangle{G}{H}{I}\),

GH=42, HI=17, IG=48

\(\displaystyle\triangle{L}{M}{N}\),

LM=21, MN=10, NL=30

Step 3

We know that if two triangles are similar then their sides are in equal ratio.

if \(\displaystyle\triangle{G}{H}{I}\ {\quad\text{and}\quad}\ \triangle{L}{M}{N}\) are similar then,

\(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{G}{I}}}{{{L}{N}}}}\)

Here,

\(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}={\frac{{{42}}}{{{21}}}}={2}\)

\(\displaystyle{\frac{{{H}{I}}}{{{M}{N}}}}={\frac{{{17}}}{{{10}}}}={1.7}\)

\(\displaystyle{\frac{{{G}{I}}}{{{L}{N}}}}={\frac{{{48}}}{{{30}}}}={1.6}\),

That means, \(\displaystyle{\frac{{{G}{H}}}{{{L}{M}}}}\ne{q}{\frac{{{H}{I}}}{{{M}{N}}}}\ne{q}{\frac{{{G}{I}}}{{{L}{N}}}}\)

Hence given two triangles are not similar, \(\displaystyle\triangle{G}{H}{I}{n}\sim\triangle{L}{M}{N}\)

Answer : These triangles are not similar.