Asquare is dilated by a scale factor of 1.25 to create a new square. how does the area of the new square compare with the area of the original shape?

the area of the new square is 1.5625 times the area of the original shape.

Justification:

Since, the square is dilated by a scale factor of 1.25 to create the new square, each side length of the new square is 1.25 times the side length of the original square. So being the area the product of two sides, the new area will be 1.25 × 1.25 = 1.5625 times the original area.

Algebraically, you can see it in this way:

Length of the sides of the original square: xArea of the original square: A = x²Length of the sides of the new square = 1.25xArea of the new square (1.25x)² = (1.25)² x² = (1.5625) x² = (1.5625)A

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

11 mintues is the naswer