Question

the area of this rhombus is 50 square feet. one of its diagonals is 20 feet. what is the length of the missing diagonal, d? feet

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 \(A = 50\) square feet and \(d_1=20\) feet. Substitute into \(A=\frac{1}{2}d_1d_2\), we get \(50=\frac{1}{2}\times20\times d_2\).

Step3: Solve for \(d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times20\times d_2 = 10d_2\). Then the equation becomes \(10d_2=50\). Divide both sides by 10: \(d_2=\frac{50}{10}=5\).

Answer:

5