Question 1: For this case, the first thing to do is find the side of the square. We have then that the perimeter is: P = 4L Clearing L: L = P / 4 Substituting values: L = 48/4 L = 12 We now look for the length of the diagonal. for this we use the Pythagorean theorem: d = root ((L) ^ 2 + (L) ^ 2) d = root ((12) ^ 2 + (12) ^ 2) d = 16.97 feet Rounding: d = 17 feet Answer: G option d = 17 feet
Question 2: For this case we have the following equation: 2a - 6 + 5a = 3a + 10 We solve the equation. To do this, we clear to. 2a + 5a + 3a = 10 + 6 a * (2 + 5 + 3) = 16 10a = 16 a = 16/10 a = 1.6 Rounding off we have: a = 2 Answer: a = 2
Question 3: For this case the coordinates of the midpoint are: C = (((x1 + x2) / 2), ((y1 + y2) / 2)) Substituting values: C = (((-3 + 4) / 2), ((2 + 8) / 2)) Rewriting we have: C = ((1/2), (10/2)) C = (0.5, 5) We use the formula of distance between points: d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2) Then, the distance AC is: AC = root ((0.5 - (- 3)) ^ 2 + (5-2) ^ 2) AC = 4.61 units Answer: AC = 4.61 units option A
