Find the area of a rhombus having each side equal to 15 cm and one of whose diagonals is 24 cm
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Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12
Let BO = x and AB = 15 cm (given)
By Pythagorean theorem
c2 = a2 + b2
225 = 144 + x²
x2 = 225 – 144
x2 = 81
x = 9 cm
BO = 9 cm
Diagonal BD = 2 x 9= 18cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 18
Area = 216sq.cm
AC = 24 ⇒ AO = 12
Let BO = x and AB = 15 cm (given)
By Pythagorean theorem
c2 = a2 + b2
225 = 144 + x²
x2 = 225 – 144
x2 = 81
x = 9 cm
BO = 9 cm
Diagonal BD = 2 x 9= 18cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 18
Area = 216sq.cm
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