Question

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The shorter diagonal of a rhombus measures 18cm. The side of the rhombus measures 41cm. Find the length of the longer diagonal.

Answer 1

80 cm

Explanation:

The diagonals divide the rhombus into four congruent triangles. The height of each triangle is 18/2 = 9, and the hypotenuse is 41. Using Pythagorean theorem, the width of each triangle is:

c² = a² + b²

41² = 9² + x²

x = 40

Therefore, the longer diagonal is 2×40 = 80.