Answer:
- The length of the diagonals is 0.3 m and 0.4 m
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Let the diagonals of the rhombus be 3x and 4x.
We know that, in a rhombus, the diagonals bisect each other at right angles. This divides the rhombus into 4 congruent right triangles.
Given that the perimeter is 1 meter, the side length of the rhombus is 1/4 meters, since all sides of a rhombus are congruent.
Using the Pythagorean theorem for one of the right triangles, we get the equation:
- (3x/2)² + (4x/2)² = (1/4)²
- 9x²/4 + 16x²/4 = 1/16
- 9x² + 16x² = 1/4
- 25x² = 1/4
- x² = 1/100
- x = 0.1 (taking positive root only as distance)
Find the length of the diagonals:
- 3x = 3(0.1) = 0.3 meters
- 4x = 4(0.1) = 0.4 meters
