Question

DKLM is a rhombus.

If AM = 4x, AK = 5x-3, and DL = 10, find the length of KL
A) 7

B) 10

C) 13

D) 15

E) 17

Answer 1

To find the length of KLA: set up an equation using the properties of a rhombus, solve for x, and substitute the value back to find KL.

Step-by-step explanation:

To find the length of KLA, we need to use the properties of a rhombus. In a rhombus, all four sides are equal in length. So, we can set up the following equation:

AM = AK + KL + LA

4x = (5x-3) + KL + (5x-3)

10x - 6 = KL

Since DKLM is a rhombus, KL is equal to DL. So, we can substitute the value of DL into the equation:

10x - 6 = 10

10x = 16

x = 1.6

Finally, we can substitute the value of x back into the equation to find KL:

KL = 10x - 6 = 10(1.6) - 6 = 16 - 6 = 10

Therefore, the length of KL is 10.