Answer:
AB = AC = 172.2 feet , CB = 200 feet
Isosceles triangle
Perimeter of the park = 544.4 feet
∠CAB = 71° , ∠ACB = ∠ABC = 54.4°
Explanation:
The actual side lengths of the triangular plot of land:
The length of AC = inches
The length of AB = inches
The length of CB = 11 inches - 1 inch = 10 inches
The type of triangle formed by the intersection of the three streets:
Since AC = AB , the triangle ACB is an isosceles triangle.
Actual measure of each angle of the triangle:
∠ACB = ∠ABC = 3x + 12.5 = 3x + 12.5 (isosceles triangle has two equal angles)
(5x + 1)° + 2(3x + 12.5)° = 180° (angles in a triangle adds up to 180°)
5x + 6x + 1 + 25 = 180°
11x = 154
x = 14
∠CAB = (5(14) + 1)° = 71°
∠ACB = ∠ABC = 3(14) + 12.5 = 54.5°
The actual side lengths of the triangular plot of land:
Given; 1 inch = 20 feet
CB = 10 inches = 200 feet
i.e
AB = AC = ( 200 × sin 54.5°) ÷ sin 71° = 172.2 feet (correct to one decimal place)
The amount of fencing needed to surround the city park
:
The perimeter of the city pack = CB + AB + AC = 200 feet + 2(172.2) feet = 544.4 feet