This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To estimate the perimeter of the land, we need to calculate the length of each segment forming its boundary and then sum them up. We will use the Pythagorean theorem (distance formula) for each segment. Step 1: Define the coordinates of the points. Let point A be the origin (0,0). The baseline AB lies along the x-axis. • A = (0,0) • B = (56,0) (since the total length of the baseline is 16+28+12 = 56 units) The other points are defined by their offsets from the baseline: • Point Q: 16 units from A along the baseline, 8 units to the left (negative y-direction). So, Q = (16, -8). • Point P: 16+28 = 44 units from A along the baseline, 16 units to the left (negative y-direction). So, P = (44, -16). • Point R: 16 units from A along the baseline, 18 units to the right (positive y-direction). So, R = (16, 18). • Point S: 16+10 = 26 units from A along the baseline, 32 units to the right (positive y-direction). So, S = (26, 32). Step 2: Calculate the length of each segment using the distance formula d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2). Length QA*: A = (0,0), Q = (16, -8) QA = sqrt((16-0)^2 + (-8-0)^2) = sqrt(16^2 + (-8)^2) = sqrt(256 + 64) = sqrt(320) ≈ 17.8885 Length QP*: Q = (16, -8), P = (44, -16) QP = sqrt((44-16)^2 + (-16-(-8))^2) = sqrt(28^2 + (-8)^2) = sqrt(784 + 64) = sqrt(848) ≈ 29.1204 Length PB*: P = (44, -16), B = (56, 0) PB = sqrt((56-44)^2 + (0-(-16))^2) = sqrt(12^2 + 16^2) = sqrt(144 + 256) = sqrt(400) = 20.0000 Length BS*: B = (56, 0), S = (26, 32) BS = sqrt((26-56)^2 + (32-0)^2) = sqrt((-30)^2 + 32^2) = sqrt(900 + 1024) = sqrt(1924) ≈ 43.8634 Length SR*: S = (26, 32), R = (16, 18) SR = sqrt((16-26)^2 + (18-32)^2) = sqrt((-10)^2 + (-14)^2) = sqrt(100 + 196) = sqrt(296) ≈ 17.2047 Length RA*: R = (16, 18), A = (0,0) RA = sqrt((0-16)^2 + (0-18)^2) = sqrt((-16)^2 + (-18)^2) = sqrt(256 + 324) = sqrt(580) ≈ 24.0832 Step 3: Sum the lengths of all segments to find the total perimeter. Perimeter = QA + QP + PB + BS + SR + RA Perimeter ≈ 17.8885 + 29.1204 + 20.0000 + 43.8634 + 17.2047 + 24.0832 Perimeter ≈ 152.1602 Step 4: Round the perimeter to the nearest meter. Perimeter ≈ 152 meters The estimated perimeter of the land is 152 meters. The perimeter of the land is 152 meters. What's next?