Question

efgh is a rhombus. given eg = 16 and fh = 12, what is the length of one side of the rhombus? 6 units 8 units 10 units 14 units

Explanation:

Step1: Find half - lengths of diagonals

In a rhombus, the diagonals bisect each other.
If \(EG = 16\), then half of \(EG\), say \(a=\frac{EG}{2}=\frac{16}{2}=8\)
If \(FH = 12\), then half of \(FH\), say \(b = \frac{FH}{2}=\frac{12}{2}=6\)

Step2: Use the Pythagorean theorem

The sides of a rhombus and the half - diagonals form a right - triangle. Let \(s\) be the side of the rhombus.
By the Pythagorean theorem \(s=\sqrt{a^{2}+b^{2}}\)
Substitute \(a = 8\) and \(b = 6\) into the formula: \(s=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}\)

Answer:

\(10\) units (the third option)