Question

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

Explanation:

Step1: Use the property of a rhombus

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

Step2: Solve the equation for \(s\)

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

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

Substitute \(s = 45\) into the expression for \(BC\) (either \(9s + 29\) or \(10s - 16\)).
Using \(9s+29\): \(9\times45+29=405 + 29=434\).

Answer:

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