Question

5 the diagram below shows a rhombus: diagram of rhombus with sides labeled: ab=17, ad=7y+3, bc=3x+11 find the measures of the following variables (show all work on paper): x = blank y = blank

Explanation:

Step1: Use the property of a rhombus (all sides are equal)

In a rhombus, \(AB = BC=CD = DA\). So, \(AB = 17\), \(BC=3x + 11\), and \(AD = 7y+3\).
Since \(AB = BC\), we have the equation \(3x+11=17\).
Subtract 11 from both sides: \(3x=17 - 11\), so \(3x = 6\).
Divide both sides by 3: \(x=\frac{6}{3}=2\).

Step2: Use the property \(AB = AD\)

Since \(AB = 17\) and \(AD = 7y + 3\), we set up the equation \(7y+3=17\).
Subtract 3 from both sides: \(7y=17 - 3\), so \(7y = 14\).
Divide both sides by 7: \(y=\frac{14}{7}=2\).

Answer:

\(x = 2\), \(y = 2\)