In a rhombus,the diagonals measure 10 and 24. | vedclass

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(A) Let the rhombus be $ABCD$ with diagonals $AC = 24$ and $BD = 10$.In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let t

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(A) Let the rhombus be $ABCD$ with diagonals $AC = 24$ and $BD = 10$.In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the intersection point be $O$.Then,$AO = AC / 2 = 24 / 2 = 12$ and $BO = BD / 2 = 10 / 2 = 5$.In the right-angled triangle $	riangle AOB$,by the Pythagorean theorem:$AB^2 = AO^2 + BO^2$$AB^2 = 12^2 + 5^2$$AB^2 = 144 + 25 = 169$$AB = \sqrt{169} = 13$.Since all sides of a rhombus are equal,the length of each side is $13$.

In a rhombus,the diagonals measure $10$ and $24$. Then,the length of each side of the rhombus is...........

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