Question

1. what is the value of x if the quadrilateral is a rhombus? 15 5x 4x + 3 5 3 25 15

Explanation:

Step1: Recall rhombus property

In a rhombus, all sides are equal. So we can set up an equation using two - side lengths. Let's set \(4x + 3=15\) (we could also use \(5x\) and set it equal to one of the other sides, but this is a simpler equation to start with).

Step2: Solve the equation for \(x\)

Subtract 3 from both sides of the equation \(4x+3 = 15\). We get \(4x=15 - 3\), so \(4x=12\). Then divide both sides by 4: \(x=\frac{12}{4}=3\).
We can also check with the other side. If \(x = 3\), then \(5x=5\times3 = 15\), which is consistent with the side - length of 15 given in the rhombus.

Answer:

3