Question

he area of a rhombus is 65 square units. the length of one diagonal is 13 units. what is the length of the other diagonal? 5 units 10 units 6 units 12 units

Explanation:

Step1: Recall the area formula of a rhombus

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.

Step2: Substitute the known values into the formula

Given \(A = 65\) and \(d_1=13\). Substitute into \(A=\frac{1}{2}d_1d_2\), we get \(65=\frac{1}{2}\times13\times d_2\).

Step3: Solve for \(d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times13\times d_2=\frac{13d_2}{2}\). Then the equation becomes \(65=\frac{13d_2}{2}\). Multiply both sides by \(2\): \(65\times2 = 13d_2\), so \(130 = 13d_2\). Divide both sides by \(13\): \(d_2=\frac{130}{13}=10\).

Answer:

10 units