Question

The construction of $\Delta LMN$ when $MN=7$ $cm$ and $m\angle M={45}^{\circ }$ is not possible when difference of $LM$ and $LN$ is equal to:

• A. $4.5$
• B. $5.5$
• C. $6.5$
• D. $7.5$

Answer 1

The correct option is D $7.5$

The triangle inequality rule states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

In $△LMN$, if $MN=7cm$ then $LM-LN<7cm$

This is not possible, from the given options, if $LM-LN=7.5cm$

Option D.