Question

What is the length of segment LM

Answer 1

LM = 23 units

Explanation:

From figure we can see an isosceles triangle KNM

KN = NM

NL is the perpendicular from N to KM,

Therefore KL = LM

To find the value of x

From figure we can write,

14x - 3 = 25

14x = 25 + 3 = 28

x = 28/14 = 2

To find LM

LM = KL

we have KL = 9x + 5

Therefore LM = 9x + 5 = (9 * 2) + 5 = 23 units

Answer 2

LM = 23 units

Explanation:

triangle KLN and triangle MLN are congruent.

The segment LM is equal to segment LK.

Also, MN is same as KN, thus we can write:

`MN=KN\\25=14x-3\\25+3=14x\\28=14x\\x=2`

Since, x = 2, we can get the side length LM:

`LM=LK=9x+5\\LM=LK=9(2)+5\\LM=23`

Hence, LM = 23 units