Question

what are the lengths of sides kn and nm of the kite? kn = units nm = units

Explanation:

Step1: Find the value of \( y \)

In a kite, two pairs of adjacent sides are equal. So, \( 2y + 5=y + 10 \).
Subtract \( y \) from both sides: \( 2y - y+5=y - y + 10 \), which gives \( y+5 = 10 \).
Subtract 5 from both sides: \( y=10 - 5=5 \).

Step2: Calculate the length of \( KN \)

Substitute \( y = 5 \) into \( y + 10 \). So, \( KN=y + 10=5 + 10 = 15 \).

Step3: Find the value of \( x \)

Since \( 2x+6=3x - 1 \).
Subtract \( 2x \) from both sides: \( 2x-2x + 6=3x-2x - 1 \), which gives \( 6=x - 1 \).
Add 1 to both sides: \( x=6 + 1=7 \).

Step4: Calculate the length of \( NM \)

Substitute \( x = 7 \) into \( 2x + 6 \). So, \( NM=2x+6=2\times7+6=14 + 6=20 \).

Answer:

\( KN = 15 \) units
\( NM = 20 \) units