Question

ABCD is a rhombus whose diagonals meet at O.if AB=10cm and BD=12cm.find the length of the diagonal AC?
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Answer 1

$\huge\underline\mathrm{GivEn:-}$

↪ABCD is a rhombus whose diagonals meet at O

↪ AB = 10 cm

↪ BD = 12 cm

$\huge\underline\mathrm{Need\:To\:Find:-}$

↪ find the length of the diagonal AC = ?

$\huge\underline\mathrm{SoLution:-}$

Let the side to find be 'x' cm

The diagonals of triangle intersect at O. So, the side BD is divided into two equal parts

$\implies$ BO = OD

BO = 6 cm

In Triangle ABO, we need to apply Pythagoras theorem

Hypotenuse² = base² + perpendicular²

According to question :-

$\implies$ (10)² = (6)² + (x)²

$\implies$ 100 = 36 + x²

$\implies$ x² = 100 - 36

$\implies$ x² = 64

$\huge{\boxed{\bf{x = 8 cm}}}$

$\huge\underline\mathrm{ThAnKs...}$