Question

in rectangle klmn, km = 11√41 and lm/mn = 5/4. what is the length of kl?

Explanation:

Step1: Let the length \(LM = 5x\) and \(MN=4x\)

Since \(\frac{LM}{MN}=\frac{5}{4}\), we can use the property of proportion.

Step2: Apply the Pythagorean theorem in right - triangle \(LMN\)

In rectangle \(KLMN\), \(KM\) is the diagonal. By the Pythagorean theorem \(KM^{2}=LM^{2}+MN^{2}\). Substitute \(LM = 5x\), \(MN = 4x\) and \(KM=11\sqrt{41}\) into the formula: \((11\sqrt{41})^{2}=(5x)^{2}+(4x)^{2}\).

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Step3: Find the length of \(KL\)

Since \(KL = MN\) (opposite sides of a rectangle are equal) and \(MN = 4x\), substitute \(x = 11\) into \(4x\). So \(KL=4\times11\)

Answer:

\(44\)