The perimeter of a rhombus is 52 m and its shorter diagonal is 10 m. The length of the longer diagonal is
Detailed Explanation:
A rhombus has all sides equal. With perimeter 52 m, each side = 52 ÷ 4 = 13 m. Diagonals of a rhombus bisect each other at right angles, forming four right triangles.
Taking half of the shorter diagonal = 10 ÷ 2 = 5 m and side = 13 m, applying Pythagoras theorem: half of longer diagonal = √(13² − 5²) = √(169 − 25) = √144 = 12 m. Full longer diagonal = 12 × 2 = 24 m.
Therefore, the longer diagonal is 24 m, making Option 4 the correct answer.
Question 3 of 3 Mensuration
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The lengths of the diagonals of a rhombus are 10 cm and 24 cm. Its perimeter is
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