Question

what is the value of y? 3 4 5 6

Explanation:

Step1: Identify equal sides in rectangle

In a rectangle, opposite sides are equal. So the vertical side with length 10 is equal to the vertical side \(2y + 4\).
\[10 = 2y + 4\]

Step2: Solve for y

Subtract 4 from both sides:
\[10 - 4 = 2y\]
\[6 = 2y\]
Divide both sides by 2:
\[y=\frac{6}{2}=3\] Wait, no, wait. Wait, maybe I made a mistake. Wait, no, the vertical sides: left side is 10, right side is \(2y + 4\). So \(10 = 2y + 4\). Subtract 4: \(6 = 2y\), so \(y = 3\)? But wait, let's check again. Wait, maybe the horizontal sides: top is 18, bottom is \(10 + 2x\), but we need vertical. Wait, left vertical is 10, right vertical is \(2y + 4\). So \(10 = 2y + 4\). Then \(2y = 10 - 4 = 6\), so \(y = 3\). But wait, the options have 3 as an option. Wait, but let's re-examine. Wait, maybe I misread the diagram. Wait, the left side is 10, right side is \(2y + 4\). So they should be equal. So \(10 = 2y + 4\). Solving: \(2y = 10 - 4 = 6\), so \(y = 3\). So the answer is 3.

Wait, but let me check again. Maybe the vertical sides: yes, in a rectangle, opposite sides are congruent. So left side length is 10, right side length is \(2y + 4\). So set equal: \(10 = 2y + 4\). Subtract 4: \(6 = 2y\), divide by 2: \(y = 3\). So that's correct.

Answer:

3 (corresponding to the option "3")