Question

A rhombus with vertices L, M, K, and F that looks like a diamond.
If LA¯¯¯¯¯¯¯=−3x+4 and LK¯¯¯¯¯¯¯¯=−5x , what value of LK¯¯¯¯¯¯¯¯ would be required for LMKF to be a rhombus?

(1 point)
Responses

−8
negative 8

10
10

40
40

2

Answer 1

In a rhombus, all sides are of equal length. This means that the lengths of segments \( LA \) and \( LK \) must be equal:

\[
LA = LK
\]

Given that:

\[
LA = -3x + 4
\]
\[
LK = -5x
\]

We need to set these two expressions equal to each other:

\[
-3x + 4 = -5x
\]

Now, let's solve for \( x \):

\[
4 = -5x + 3x
\]
\[
4 = -2x
\]
\[
x = -2
\]

Now, we can substitute \( x = -2 \) back into either expression to find the length of \( LK \):

Using \( LK \):

\[
LK = -5(-2) = 10
\]

Thus, for \( LMKF \) to be a rhombus, the length of \( LK \) must be:

\[
\boxed{10}
\]