Final answer:
To construct a rhombus with 8cm sides and a 10cm diagonal, draw the diagonal, find its midpoint, use it to locate the vertices, and connect them. To find the other diagonal, apply the Pythagorean theorem to half the known diagonal and a side of the rhombus, resulting in a second diagonal of approximately 12.48cm.
Step-by-step explanation:
To construct a rhombus where each side is 8cm and one diagonal is 10cm, follow these steps:
- Draw a line segment of 10cm; this will be one of your diagonals.
- Find the mid-point of this line and label it. This point will be the center of the rhombus.
- With the center as the pivot, use a compass set to 8cm to draw arcs above and below the line on both ends.
- The points where the arcs intersect the line segment will be two opposite vertices of your rhombus.
- Use the compass to draw arcs from these vertices with a radius of 8cm to determine the position of the remaining two vertices.
- Connect the vertices to form the rhombus.
To find the length of the other diagonal, notice that the rhombus is symmetrical, and the diagonals bisect each other at right angles. Apply the Pythagorean theorem to one of the right-angled triangles formed by the diagonals of the rhombus:
If the half of the known diagonal is 5cm (since 10cm is the total length), and the side of the rhombus is 8cm, the other half-diagonal (d/2) can be found by:
d/2 = √(8^2 - 5^2)
= √(64 - 25)
= √39
≈ 6.24cm
Thus, the length of the second diagonal is approximately 12.48cm.