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2 years ago

If JL=18, NK=12, and ML=10, find the perimeter of JKLM A. 42 B. 45 C. 50 D. 56

Mathematics

1 answer:

snow_lady [41]2 years ago

7 0

Answer:

The perimeter of the kite JKLM is 50 units ⇒ C

Step-by-step explanation:

The longest diagonal of the kite is its axis of symmetry which means the longest diagonal divides the kite into two congruent triangles

∵ JKLM is a kite

∵ KM is the longest diagonal

∴ KM is divides the kite into two congruent triangles

∴ Δ JKM is congruent to Δ LKM

∴ JK = LK

∴ JM = ML

∵ ML = 10 units

∴ JM = 10 units

∵ The diagonals of the kite are perpendicular

∴ KM ⊥ JL

∵ KM and JL intersected at N

∴ m∠JNK = 90°

∵ KM is the axis of symmetry of kite JKLM

∴ KM bisects JL at N

∴ JN = NL = $\frac{1}{2}$ JL

∵ JL = 18 units

∴ JN = $\frac{1}{2}$ (18)

∴ JN = 9 units

In Δ JNK

∵ m∠JNK = 90°

∵ JN = 9 units

∵ NK = 12 units

- By using Pythagoras Theorem

∵ (JK)² = (JN)² + (NK)²

∴ (JK)² = (9)² + (12)²

∴ (JK)² = 81 + 144

∴ (JK)² = 225

- Take √ for both sides

∴ JK = 15 units

∵ Jk = LK

∴ Lk = 15 units

∵ The perimeter of the kite is the sum of its 4 sides

∴ P = JK + KL + LM + MJ

∵ JK = LK = 15

∵ JM = ML = 10

∴ P = 15 + 15 + 10 + 10

∴ P = 50

The perimeter of the kite JKLM is 50 units

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