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Find the Side Length with 3-Digit Square Root

Find the Side Length with 3-Digit Square Root
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2019-01-25 05:57
PolygonCoordinate GeometryGeometric Construction
This example demonstrates finding the side length with a 3-digit square root. Key math concepts include square roots and addition. Using GeoGebra commands like Polygon and Text, a geometric figure is constructed. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0, 10), (10, 10), (10, 0)) → Tot, f, g, h, i
  2. Polygon((0, 0), (((10 / side * 100) * c), 0), 4) → C
  3. Polygon((((10 / side * 100) * c), 0), ((10 / side * ((100 * c) + (10 * d))), 0), ((10 / side * ((100 * c) + (10 * d))), ((10 / side * 100) * c)), (((10 / side * 100) * c), ((10 / side * 100) * c))) → Dl, j, k, l, m
  4. Polygon((0, ((10 / side * 100) * c)), (0, (10 / side * ((100 * c) + (10 * d)))), (((10 / side * 100) * c), (10 / side * ((100 * c) + (10 * d)))), (((10 / side * 100) * c), ((10 / side * 100) * c))) → Dt, n, p, q, r
  5. Polygon((((10 / side * 100) * c), ((10 / side * 100) * c)), ((10 / side * ((100 * c) + (10 * d))), ((10 / side * 100) * c)), 4) → Dc
  6. Polygon(((10 / side * ((100 * c) + (10 * d))), 0), (10, 0), (10, ((10 / side * 100) * c)), ((10 / side * ((100 * c) + (10 * d))), ((10 / side * 100) * c))) → Ul, s, t, a, b
  7. Polygon((0, (10 / side * ((100 * c) + (10 * d)))), (0, 10), (((10 / side * 100) * c), 10), (((10 / side * 100) * c), (10 / side * ((100 * c) + (10 * d))))) → Ut, e, f_1, g_1, h_1
  8. Polygon(((10 / side * ((100 * c) + (10 * d))), ((10 / side * 100) * c)), (10, ((10 / side * 100) * c)), (10, (10 / side * ((100 * c) + (10 * d)))), ((10 / side * ((100 * c) + (10 * d))), (10 / side * ((100 * c) + (10 * d))))) → Ulc, i_1, j_1, k_1, l_1
  9. Polygon((((10 / side * 100) * c), (10 / side * ((100 * c) + (10 * d)))), (((10 / side * 100) * c), 10), ((10 / side * ((100 * c) + (10 * d))), 10), ((10 / side * ((100 * c) + (10 * d))), (10 / side * ((100 * c) + (10 * d))))) → Utc, m_1, n_1, p_1, q_1
  10. Polygon(((10 / side * ((100 * c) + (10 * d))), (10 / side * ((100 * c) + (10 * d)))), (10, (10 / side * ((100 * c) + (10 * d)))), 4) → Ucc
  11. Text((100 * c), (((5 / side * 100) * c), -0.5)) → texto1
  12. Text((10 * d), ((10 / side * ((100 * c) + (5 * d))), -0.5)) → texto2
  13. Text(u, ((10 / side * ((100 * c) + (10 * d) + u / 2)), -0.5)) → texto3

AI Drawing Prompt Reference

Draw a 10x10 square, then construct a smaller square inside it with side length equal to 100 times c plus 10 times d. Add labels at each vertex to mark the values of c, d, and a variable u. Ensure all sides of the smaller squares are parallel to the sides of the larger square.
The prompt above was compiled from the original drawing commands and is for reference only.