The city council is planning a new city park on a triangular plot of landformed by three intersecting streets.The designer placed the triangle on a grid to determine the side lengths andangle measures needed for the purchase and placement of a fencesurrounding the park. Each unit on the grid is one inch, which represents20 feet of actual length.The measure of angle CAB in the designer’s diagram is (5x + 1)°, and themeasure of angle ACB is (3x + 12.5)°.Create a report that provides a detaileddescription of the park. Include the following in your report:• the actual side lengths of the triangular plot of land• the type of triangle formed by the intersection of the three streets• the amount of fencing needed to surround the city park• the actual measure of each angle of the triangle

Answer:AB = AC = 172.2 feet , CB = 200 feetIsosceles trianglePerimeter of the park = 544.4 feet∠CAB = 71° , ∠ACB = ∠ABC = 54.4°Step-by-step explanation:The actual side lengths of the triangular plot of land:The length of AC =  inchesThe length of AB =  inchesThe length of CB = 11 inches - 1 inch = 10 inchesThe 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 = 154x = 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 feetCB = 10 inches = 200 feeti.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