ARITHMETIC AND ALGEBRA REVIEW ord problem on optimizing an area or perimeter 15 s to paint a rectangular region of a wall with one layer of paint. She has 20 ft of tape to tape around the border o ng three regions with lengths of 3 ft, 4 ft, and 5 A. egion she paints. She he questions below to find which of these regions would require the most paint. in the table to find the width and the area for each region. X 5 Х ? Length Width Area Region #1 3 ft ft 2 fit Region = 2 4 ft ft ft Region #3 5 ft ft Ift 2 fit ch of these regions would require the most paint? O Region #1 Region #2 O Region #3

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