Question

1. klmn ~ pqrs; find x

Explanation:

Step1: Identify corresponding sides

Since \( KLMN \sim PQRS \), their corresponding sides are proportional. The side \( LM = 4x + 4 \) corresponds to \( RQ = 48 \), and \( KN = 7x - 9 \) corresponds to \( SP = 60 \). So we set up the proportion \(\frac{LM}{RQ}=\frac{KN}{SP}\).

Step2: Substitute values into proportion

Substitute \( LM = 4x + 4 \), \( RQ = 48 \), \( KN = 7x - 9 \), and \( SP = 60 \) into the proportion: \(\frac{4x + 4}{48}=\frac{7x - 9}{60}\).

Step3: Cross - multiply

Cross - multiply to get \( 60(4x + 4)=48(7x - 9) \).

Step4: Expand both sides

Expand the left side: \( 60\times4x+60\times4 = 240x + 240 \). Expand the right side: \( 48\times7x-48\times9=336x - 432 \). So the equation becomes \( 240x + 240 = 336x - 432 \).

Step5: Solve for x

Subtract \( 240x \) from both sides: \( 240=336x - 240x-432 \), which simplifies to \( 240 = 96x - 432 \). Add 432 to both sides: \( 240 + 432=96x \), so \( 672 = 96x \). Divide both sides by 96: \( x=\frac{672}{96}=7 \).

Answer:

\( x = 7 \)