Question

these rectangles are similar. which proportion does not show the correct relationship between these two figures?
\\( \frac { k l } { q p } = \frac { m l } { q r } \\)
\\( \frac { k l } { q p } = \frac { n p } { n r } \\)
\\( \frac { k j } { p n } = \frac { m j } { r n } \\)
\\( \frac { l m } { m j } = \frac { r q } { n r } \\)

Explanation:

Step1: Recall the property of similar rectangles

For similar rectangles, the ratios of corresponding sides are equal.

Step2: Analyze each option

• Option 1: $\frac{KL}{QP}=\frac{ML}{QR}$. Since $KL$ and $QP$ are corresponding lengths, $ML$ and $QR$ are corresponding widths, this ratio is correct.
• Option 2: $\frac{KL}{QP}=\frac{NP}{NR}$. But $NP$ is a width and $NR$ is a length, and $KL$ and $QP$ are lengths. This ratio is incorrect as it mixes length - width correspondence wrongly.
• Option 3: $\frac{KJ}{PN}=\frac{MJ}{RN}$. $KJ$ and $PN$ are widths, $MJ$ and $RN$ are lengths. This ratio is correct.
• Option 4: $\frac{LM}{MJ}=\frac{RQ}{NR}$. $LM$ and $RQ$ are lengths, $MJ$ and $NR$ are widths. This ratio is correct.

Answer:

$\frac{KL}{QP}=\frac{NP}{NR}$