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: Recall rhombus properties

The diagonals of a rhombus are perpendicular bisectors of each other. So if \(EG = 16\) and \(FH=12\), the half - lengths of the diagonals are \(\frac{EG}{2}=8\) and \(\frac{FH}{2} = 6\).

Step2: Apply Pythagorean theorem

Let the half - lengths of the diagonals be \(a = 6\) and \(b = 8\). The side \(s\) of the rhombus can be found using the Pythagorean theorem \(s=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 6\) and \(b = 8\) into the formula: \(s=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Answer:

C. 10 units