A rhombus has an area of 2016 sq cm and a side of 65 cm. What are the lengths of its diagonals________?
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Answer: B. 126cm,32cm
Explanation
The geometric relationship linking a rhombus's side length and diagonals is given by side squared equaling the sum of half-diagonal squares. Testing the diagonal pair of one hundred twenty-six and thirty-two yields an area of one-half times product equal to twenty-one sixteen. Substituting these diagonal halves into the Pythagorean relation successfully satisfies the sixty-five centimeter side length. The diagonals of a rhombus intersect each other at right angles, dividing the shape into four congruent right triangles. The side of a rhombus forms the hypotenuse of the right triangle created by the bisecting diagonals. Area of a rhombus can also be calculated directly as one-half the product of its two diagonal lengths.
Option A fails to produce the correct area product of twenty-one sixteen when multiplied together. Option C fails to satisfy the right-triangle side length equation when tested with the given side of sixty-five. Option D produces an area calculation that does not match the specified two thousand sixteen square centimeters.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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