Pregunta
19. (51) The perimeter of \( \triangle J K L \) is 32 inches, and \( \angle J \equiv \angle K \). If \( J K=12 \) inches, determine the length of segment \( J L \).
Ask by Vargas Olson. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
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The length of segment JL is 10 inches.
Solución
Since ∠J is equal to ∠K, the sides opposite these angles in triangle JKL are congruent. That means the side opposite ∠J (which is segment KL) is congruent to the side opposite ∠K (which is segment JL).
Given:
• JK = 12 inches
• Let JL = KL = x inches
The perimeter of the triangle is the sum of its three sides:
JK + KL + JL = 32 inches
12 + x + x = 32
Combine like terms:
12 + 2x = 32
Subtract 12 from both sides:
2x = 20
Divide both sides by 2:
x = 10 inches
Thus, the length of segment JL is 10 inches.
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Simplifique esta solución Beyond the Answer
In triangle \( JKL \), since \( \angle J \equiv \angle K \), it implies that triangle \( JKL \) is isosceles with \( J L = K L \). Given the perimeter of the triangle is 32 inches, we can represent the sides as follows: - \( J K = 12 \) inches - \( J L = K L = x \) The equation for the perimeter is: \[ J K + J L + K L = 32 \] Substituting the values, we have: \[ 12 + x + x = 32 \] This simplifies to: \[ 12 + 2x = 32 \] Subtract 12 from both sides: \[ 2x = 20 \] Now, divide both sides by 2: \[ x = 10 \] Thus, the lengths of segments \( J L \) and \( K L \) are both 10 inches. Therefore, the length of segment \( J L \) is \( \boxed{10} \) inches.
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