Question

the area of this rhombus is 0.625 square feet. one of its diagonals is 0.5 feet. what is the length of the missing diagonal, d? feet

Explanation:

Step1: Recall 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

We know that \(A = 0.625\) square feet and \(d_1=0.5\) feet. Plugging these into the formula \(0.625=\frac{1}{2}\times0.5\times d_2\).

Step3: Solve for \(d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times0.5=\frac{0.5}{2}=0.25\). So the equation becomes \(0.625 = 0.25d_2\). Then, divide both sides by \(0.25\): \(d_2=\frac{0.625}{0.25}\). Since \(\frac{0.625}{0.25}=\frac{625}{250}= 2.5\).

Answer:

\(2.5\)