The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle? If w represents the width of the rectangle, then which equation could be used to solve for w? 2(4 w + 3) = 62
( w + 1)(3w + 2)=62
2(3 w + 3) = 62

Pretty sure it’s the second option because length would be 3w+2
and width would be w+1 and with area you have to multiply so it would just be the (w+1)(3w+2)

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