Question

what is the side of a rhombus whose diagonal is D1 and D2​

Answer 1

$\bf\textsf{Concept used:}$

$\textsf{Diagonals of a rhombus bisect each other}$

$\textsf{Diagonals of a rhombus intersect at right angles}$

$\bf\textsf{Solution:}$

$\textsf{Let x be length of the side the of the rombus}$

$\textsf{By pythagoras theorem,}$

$\mathsf{x^2=(\dfrac{D_1}{2})^2+(\dfrac{D_2}{2})^2}$

$\mathsf{x^2=\dfrac{{D_1}^2}{4}+\dfrac{{D_2}}{4}}$

$\mathsf{x^2=\dfrac{{D_1}^2+{D_2}^2}{4}}$

$\textsf{Taking square root, we get}$

$\mathsf{x=\sqrt{\dfrac{{D_1}^2+{D_2}^2}{4}}}$

$\implies\bf\mathsf{x=\dfrac{1}{2}\sqrt{{D_1}^2+{D_2}^2}}$

$\therefore\bf\textsf{Length of the side of the rhombus having diagonals}$

$\mathsf{D1}\;\textsf{and}\;\mathsf{D2}\;\textsf{is}\;\mathsf{\dfrac{1}{2}\sqrt{{D_1}^2+{D_2}^2}}$

Answer 2

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