A rhombus with vertices L, M, K, and F that looks like a diamond.

Question

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:

\[ \boxed{10} \]