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 \(y\)

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: Find the length of \(KN\)

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

Step3: Solve for \(x\)

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: Find 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