Question

jklm is a rhombus with an area of 75 square feet. diagonal \\(\overline{km}\\) is 15 feet long. what is the length of \\(\overline{oj}\\)? (image of rhombus jklm with diagonals intersecting at o, not drawn to scale) options: a) 5 ft, b) 7 ft, c) 8 ft, d) 12 ft

Explanation:

Step1: Find the length of the other diagonal

The area formula of a rhombus is \(A=\frac{1}{2}d_1d_2\), where \(d_1\) and \(d_2\) are the lengths of the diagonals.
Given \(A = 75\) square feet and \(d_1=KM = 15\) feet.
Substitute into the formula: \(75=\frac{1}{2}\times15\times d_2\).
Solve for \(d_2\):

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Step2: Use the property of rhombus diagonals (bisect each other at right - angles)

In a rhombus, the diagonals bisect each other. So \(OK=\frac{KM}{2}=\frac{15}{2} = 7.5\) feet and \(OJ=\frac{d_2}{2}\) (since \(d_2\) is the other diagonal).
Since \(d_2 = 10\) feet, \(OJ=\frac{10}{2}=5\) feet.

Answer:

A. \(5\) ft