The Jackson family plans to purchase a large farm. To protect their new land, they've hired a land surveyor. The surveyor has pinpointed the boundaries of the property so that the family can build a fence along the perimeter. The image shows the markers and dimensions of the plot of land. The figure shows a rectangle with a length of 5000 feet and a width of 2000 feet. A semicircle is adjacent to the top side of the rectangle. Another semicircle is adjacent to the right side of the rectangle. he fence will be built along the perimeter of the land. How much fencing must the Jackson family purchase? Use π=3.14. If necessary, round to the nearest tenth.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Then just do it (lol)