Question

the area of this rhombus is 10 square meters. one of its diagonals is 5 meters. what is the length of the missing diagonal, d? meters

Explanation:

Step1: Recall the area formula for a rhombus

The area formula for 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

We know that \(A = 10\) square meters and \(d_1=5\) meters. Substituting into the formula \(10=\frac{1}{2}\times5\times d_2\).

Step3: Solve for \(d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times5\times d_2=\frac{5d_2}{2}\). Then, solve the equation \(10=\frac{5d_2}{2}\) for \(d_2\). Multiply both sides by \(2\) to get \(20 = 5d_2\). Divide both sides by \(5\), so \(d_2=\frac{20}{5}=4\).

Answer:

\(4\)