Question

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

Explanation:

Step1: Solve for \(x\)

In a kite, two pairs of adjacent sides are equal. So, \(3x - 1=2x + 6\).
Subtract \(2x\) from both sides: \(3x-2x-1 = 2x-2x + 6\), which gives \(x-1=6\).
Add \(1\) to both sides: \(x=6 + 1=7\).

Step2: Find the length of \(NM\)

Substitute \(x = 7\) into the expression for \(NM\) (\(NM=2x + 6\)).
\(NM=2\times7+6=14 + 6=20\).

Step3: Solve for \(y\)

Also, \(2y+5=y + 10\).
Subtract \(y\) from both sides: \(2y - y+5=y - y+10\), which gives \(y+5=10\).
Subtract \(5\) from both sides: \(y=10 - 5 = 5\).

Step4: Find the length of \(KN\)

Substitute \(y = 5\) into the expression for \(KN\) (\(KN=y + 10\)).
\(KN=5+10=15\).

Answer:

KN = 15 units, NM = 20 units