Questions: If GK=5c-31 and IK=7c-53, find IK in rectangle GHIJ. IK=

If GK=5c-31 and IK=7c-53, find IK in rectangle GHIJ. IK=
Transcript text: If $G K=5 c-31$ and $I K=7 c-53$, find $I K$ in rectangle $G H I J$. \[ I K= \]
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Solution

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Solution Steps

Step 1: Setting up the equation

The diagonals of a rectangle are congruent and bisect each other. This means that GK and IK are equal in length. Thus, we can set up the equation 5c - 31 = 7c - 53.

Step 2: Solving for c

To solve for c, we can first subtract 5c from both sides of the equation: -31 = 2c - 53. Then, add 53 to both sides: 22 = 2c. Finally, divide both sides by 2 to get c = 11.

Step 3: Substituting c into the expression for IK

Substitute the value of c (11) into the expression for IK: IK = 7(11) - 53 = 77 - 53 = 24.

Final Answer: The length of IK is 24.

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