Question

what is the value of y? 18 10 2y + 4 10 + 2x 3 4 5 6

Explanation:

Step1: Recall rectangle side property

In a rectangle, opposite sides are equal. So the vertical sides (height) should be equal. The left vertical side is 10, and the right vertical side is \(2y + 4\). So we set up the equation: \(2y + 4 = 10\).

Step2: Solve for y

Subtract 4 from both sides: \(2y = 10 - 4\) which simplifies to \(2y = 6\). Then divide both sides by 2: \(y=\frac{6}{2}=3\). Wait, no, wait. Wait, maybe I made a mistake. Wait, no, let's check again. Wait, the left side is 10, right side is \(2y + 4\). So \(2y + 4 = 10\). Subtract 4: \(2y = 6\), so \(y = 3\)? But wait, the options have 3 as an option. Wait, but let's check the horizontal sides. The top horizontal side is 18, bottom is \(10 + 2x\). So \(10 + 2x = 18\), but we don't need x for y. So for y, since vertical sides are equal: \(2y + 4 = 10\). So \(2y = 6\), \(y = 3\). Wait, but the first option is 3. Wait, but let me check again. Wait, maybe I misread the diagram. Wait, the left side is 10, right side is \(2y + 4\). So yes, \(2y + 4 = 10\). So solving: \(2y = 10 - 4 = 6\), so \(y = 3\). Wait, but the options include 3. So that's correct.

Answer:

3 (corresponding to the option "3")