Question

Can someone help me find JL :,)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

In triangle JKL,

• KM = MJ

i.e. M is the midpoint of KJ.

• NK = NL

i.e. N is the midpoint of KL.

And

• MN = 5x - 16

• JL = 4x + 34

We know,

Midpoint Theorem

It states that

Line segment joining the mid-points of two sides of a triangle is parallel to third side and equals to half of it.

So,

According to statement,

• M is the midpoint of KJ

• N is the midpoint of KL.

Hence,

By midpoint theorem,

$\rm :\longmapsto\:JL = 2 MN$

$\rm :\longmapsto\:4x + 34 = 2(5x - 16)$

$\rm :\longmapsto\:4x + 34 = 10x -32$

$\rm :\longmapsto\:4x - 10x = - 34 -32$

$\rm :\longmapsto\: - 6x = - 66$

$\bf\implies \:x = 11$

Now,

$\rm :\longmapsto\:JL = 4x + 34 = 4 \times 11 + 34 = 78$

Additional Information :-

Converse of Midpoint theorem :-

If a line is drawn through the midpoint of one side of a triangle parallel to other side, it bisects the third side.

Answer 2

Answer:

JL = 78

Step-by-step explanation:

Given:

KN = LN

KM = JM

MN = 5x - 16

JL = 4x + 34

To find:

JL = ?

Solution:

∵ KN = LN

∴ N is the midpoint of KL.

Similarly,

∵ KM = JM

∴ M is the midpoint of KJ.

Now,

In ΔKJL,

Using the mid point theorem,

MN || JL and MN = $\sf{\dfrac{1}{2} }$ JL

Substituting the values,

$\sf{5x - 16 = \dfrac{1}{2}(4x + 34)}$

$\implies \sf{5x - 16 = 2x + 17}$

$\implies \sf{5x - 2x = 17 + 16}$

$\implies \sf{3x = 33}$

$\implies \sf{x = \dfrac{33}{3}}$

$\implies \sf{x =11}$

Now,

   $\sf{JL = 4x + 34}$

$\mapsto \sf{JL = (4 \times 11) + 34}$

$\mapsto \sf{JL = 44 + 34}$

$\mapsto \sf{JL =78}$

Hence,

JL = 78

Midpoint Theorem:

The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side .