Question

If JL = 16, KM = 4x-1, and KM is a perpendicular bisector of JL, determine which of the following values are correct. Select ALL that apply.
A.x = 3
B.JK = 11
C.KM = 15
D.KL = 17
E.Perimeter of triangle KLM = 22
F.Perimeter or triangle JKL = 50

Answer 1

*see attachment for diagram

Answer:

C.KM = 15

D.KL = 17

F.Perimeter or triangle JKL = 50

Step-by-step explanation:

Given:

JL = 16,

KM = 4x-1

JK = 6x - 7

KL = 5x - 3

✔️Thus, let's find the value of x

Since KM is a perpendicular bisector of JL, it means JM = LM = ½*16 = 8

KM in ∆KJM is equal to KM in ∆KLM.

The angles opposite the two corresponding congruent sides in both triangles are also congruent to each other. Therefore, the third corresponding side and angles would be congruent to each other.

Thus:

JK = KL

6x - 7 = 5x - 3 (substitution)

Collect like terms

6x - 5x = 7 - 3

x = 4

✔️Find JK:

JK = 6x - 7

Plug in the value of x

JK = 6(4) - 7

JK = 24 - 7

JK = 17

✔️Find KM:

KM = 4x - 1

Plug in the value of x

KM = 4(4) - 1

KM = 16 - 1

KM = 15

✔️Find KL:

KL = 5x - 3

Plug in the value of x

KL = 5(4) - 3

KL = 20 - 3

KL = 17

✔️Find the Perimeter of ∆KLM:

Perimeter of ∆KLM = KM + KL + LM

= 15 + 17 + 8

= 40

✔️Find the Perimeter of JKL:

Perimeter of ∆JKL = JK + KL + JL

= 17 + 17 + 16

= 50.

The correct values are:

C.KM = 15

D.KL = 17

F.Perimeter or triangle JKL = 50