Question

applying the definition of a rhombus
what is the value of s and the length of side bc if abcd is a rhombus?

Explanation:

Step1: Use the property of a rhombus

In a rhombus, all sides are equal. So, \(9s + 29=10s - 16\).

Step2: Solve for \(s\)

Subtract \(9s\) from both sides: \(29=s - 16\).
Add \(16\) to both sides: \(s=29 + 16=45\).

Step3: Find the length of side \(BC\)

Substitute \(s = 45\) into \(9s+29\) (or \(10s - 16\)).
\(BC=9\times45+29=405+29 = 434\) (or \(BC = 10\times45-16=450-16=434\)).

Answer:

\(s = 45\), \(BC = 434\) units.