Question

1. find x, mn, and ln given △lnm

x =
mn =
ln =
6x - 8 + 17
4x + 14

Explanation:

Step1: Set up an equation using triangle - side relationships

Assume that in \(\triangle LNM\), we can use the fact that if we consider some property (e.g., if it's an isosceles triangle or some other relationship). Let's assume \(MN = LN\). So, \(2x + 7=3x - 4\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x+7 - 2x=3x - 4-2x\), which gives \(7=x - 4\). Then add 4 to both sides: \(x=7 + 4=11\).

Step3: Find the length of \(MN\)

Substitute \(x = 11\) into the expression for \(MN\): \(MN=2x + 7=2\times11+7=22 + 7=29\).

Step4: Find the length of \(LN\)

Substitute \(x = 11\) into the expression for \(LN\): \(LN=3x - 4=3\times11-4=33 - 4=29\).

Answer:

\(x = 11\)
\(MN = 29\)
\(LN = 29\)