Question

Rhombus LMNO
has a diagonal line MO¯¯¯¯¯¯¯¯¯
. If the length of LO¯¯¯¯¯¯¯=5
units and MO¯¯¯¯¯¯¯¯¯=8
units, what is the unit length of LM¯¯¯¯¯¯¯¯¯
?(1 point) and the answer issssssss

Answer 1

In a rhombus, all sides are equal in length, and the diagonals bisect each other at right angles.

Given:
- The length of diagonal \( LO = 5 \) units
- The length of diagonal \( MO = 8 \) units

Since the diagonals bisect each other, we can find half of each diagonal:
- Half of diagonal \( LO \) is \( \frac{5}{2} = 2.5 \) units
- Half of diagonal \( MO \) is \( \frac{8}{2} = 4 \) units

Now, we can use the Pythagorean theorem to find the length of one side of the rhombus, \( LM \). The lengths of the two halves of the diagonals \( LO \) and \( MO \) form a right triangle with side \( LM \):

\[
LM^2 = (2.5)^2 + (4)^2
\]
\[
LM^2 = 6.25 + 16
\]
\[
LM^2 = 22.25
\]
\[
LM = \sqrt{22.25} \approx 4.72 \text{ units}
\]

So, the length of side \( LM \) is approximately \( 4.72 \) units.