Question

the area of this rhombus is 6 square millimeters. one of its diagonals is 4 millimeters. what is the length of the missing diagonal, d? millimeters

Explanation:

Step1: Write the formula for the area of a rhombus

The area formula of a rhombus is \(A=\frac{1}{2}d_1d_2\), where \(A\) is the area, \(d_1\) and \(d_2\) are the lengths of the diagonals.

Step2: Substitute the known values into the formula

Given \(A = 6\) square millimeters and \(d_1=4\) millimeters. Substitute into \(A=\frac{1}{2}d_1d_2\), we get \(6=\frac{1}{2}\times4\times d_2\).

Step3: Solve for \(d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times4\times d_2 = 2d_2\). Then the equation becomes \(2d_2=6\). Divide both sides by 2: \(d_2=\frac{6}{2}=3\).

Answer:

3