Question

find hi in parallelogram hijk. hi =

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So \(JK = HI\) and \(JH=IK\). Here, we use \(JK = HI\) (not relevant for calculation here, but for understanding the figure). We use the property that \(JK = HI\) (wait, no, actually we use \(JH = IK\) to find \(p\). Since \(JH=p + 25\) and \(IK = 2p-11\), we set up the equation \(2p-11=p + 25\).

$$2p-11=p + 25$$

Step2: Solve for \(p\)

Subtract \(p\) from both sides: \(2p-p-11=p - p+ 25\), which gives \(p-11 = 25\). Then add 11 to both sides: \(p-11 + 11=25 + 11\), so \(p=36\).

Step3: Find the length of \(HI\)

Since \(HI=p + 6\), substitute \(p = 36\) into the expression. Then \(HI=36+6\).

$$HI=42$$

Answer:

\(42\)