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)
LM¯¯¯¯¯¯¯¯¯=
units
Remai

Answer 1

In a rhombus, the diagonals bisect each other at right angles. To find the length of side \( LM \), we can use the properties of right triangles formed by the diagonals.

Given:
- \( LO = 5 \) units (half of diagonal \( LN \))
- \( MO = 8 \) units (half of diagonal \( MO \))

Thus, the full lengths of the diagonals are:
- \( LN = 2 \times LO = 2 \times 5 = 10 \) units
- \( MO = 2 \times MO = 2 \times 8 = 16 \) units

Now, we can use the right triangle \( LOM \) to find the length of \( LM \). By applying the Pythagorean theorem:

\[
LM^2 = LO^2 + MO^2
\]

Substituting the known lengths:

\[
LM^2 = 5^2 + 8^2
\]
\[
LM^2 = 25 + 64
\]
\[
LM^2 = 89
\]

Taking the square root:

\[
LM = \sqrt{89}
\]

Thus, the length of \( LM \) is \( \sqrt{89} \) units.

If you want to give a numerical approximation, \( \sqrt{89} \approx 9.43 \) units.

So, the answer is:

\[
LM \approx 9.43 \text{ units}
\]