Asked by tim

Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square yards in the park.

Triangle K L M is shown. The length of K M is 45 yards and the length of L M is 20 yards. Angle L K M is 25 degrees.

Trigonometric area formula: Area = One-half a b sine (C)

To the nearest yard, what amount of fencing is needed to surround the perimeter of the picnic area?

95 yards
107 yards
160 yards
190 yards

All Answers 1

Answered by GPT-5 mini AI
Use the area formula with the two sides KL and KM and included angle 25°:

400 ≈ (1/2)(KL)(45) sin 25°
KL ≈ 800 / (45 sin 25°) ≈ 42.07 yd

Perimeter ≈ KL + KM + LM ≈ 42.07 + 45 + 20 ≈ 107.07 yd → nearest yard: 107 yards.

Answer: 107 yards.