Answer:Refer to step-by-step.Step-by-step explanation:12. x = 28BC = xAB = 96AC = 100We use the Pythagorean theorem to find the value of x.a² + b² = c²x² + 96² = 100²x² + 9216 = 10000x² = 10000-9216x² = 784√x² = √784x = 2813. x = 64a² + b² = c²48² + x² = 80²2304 + x² = 6400x² = 6400 - 2304x² = 4096√x² = √4096x = 6414. YES and 25 = 25a² + b² = c²3² + 4² = 5²9 + 16 = 2525 = 25So this means that AB is tangent to the circle.15. NO and 45 ≠ 49a² + b² = c²3² + 6² = 7²9 + 36 = 4945 = 49 So this means the AB is not tangent to the circle.16. x = 4.5 and P = 52To find the value of x, we need to determine the value of our hypotenuse.QU is congruent to QT, therefore, QT = 4UR is congruent with SR, therefore, UR = 13PS is congruent to AB, therefore: 2x = 9Divide both sides by 2x = 4.5The perimeter of a triangle is:P = a + b + ca = 9 + 4 or 13b = 2(4.5) + 13 or 22c = 4 + 13 or 17P = 13 + 22 + 17P = 5217. x = 13 and P = 72TJ is congruent to UJ, therefore, TJ = 13x = 13The perimeter of a parallelogram is:P = 2(a+b)a = HR + RKb = KU + UJa = 13 + 5 or 18b = 5 + 13 or 18P = 2(18 + 18)P = 2(36)P = 7218. x = 8 and P = 80We know that part of the whole of 26 is 18 because one side is congruent to 18.to find the value of the other half, we simply subtract 18 from 26.26 - 18 = 8x is congruent to 8, therefore x = 8The line segment 14 is congruent to the opposite segment of x, therefore making the value 14.So then we have:a = 8 + 14 or 22b = 26c = 18 + 14 or 32P = a + b + cP = 22 + 26 + 32P = 8019. x = 6 and P = 52Now we have the case of x + 2 is congruent to 8.x + 2 = 8Combine like terms.x = 8 - 2x = 6Now that we have the value of x, we can simply look for the value of the line segment attached to it.4 is congruent to the line segment attached to x + 2, therefore the value is 4.To find the perimeter we have to add all sides together.P = (8+5)+(5+9)+(9+4)+(8+4)P = 5220. x = 5, y = 2, z =10, and P = 68Let's take this one step at a time.First we look for x.2x + 2 = 3x - 3Combine like terms.2x - 3x = -3 - 2-x = -5Divide both sides by -1.x = 5Now let's get the value of y.5y - 2 = 3y + 2Combine like terms.5y - 3y = 2 + 22y = 4Divide both sides by 2.y = 2Now let's look for z.34 - 2z = z + 4Combine like terms.-2z - z = 4 - 34-3z = -30Divide both sides by -3.z = 10Now that we have the values of x, y, and z. We can substitute them to find the values of our segments.2x + 22(5) + 2 = 123x - 33(5)-3 = 125y - 25(2) - 2 = 83y + 23(2) + 2 = 8z + 410 + 4 = 1434 - 2z34 - 2(10)34 - 20 = 14Now that we have our values let's look for our perimeter.P = a + b + cP = (12 + 8) + (12 + 14) + (14 + 8)P = 20 + 26 + 22P = 68