The perimeter of a rhombus is 180 cm square and one of its diagonal is 72 cm square find the length of the other siagonal and area of rhombus
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Perimeter of rhombus = 4 × side
180= 4× side
180/4 = side
45 cm = side
We know that diagonals of rhombus bisect each other at 90° .
So, diagonal 1 = 72 cm
Half of diagonal 1 =72/2
=36 cm
In ∆AOB
AB^2 = AO^2 + BO^2
45^2 = 36^2 + BO^2
2025= 1296+ BO^2
2025-1296=BO^2
729=BO^2
√729=BO
27 cm =BO
So, Second Diagonal( BD) = 2×BO
=2×27
= 54 cm
Area of rhombus = 1/2 × Diagonal 1 × Diagonal 2
=1/2 ×72 ×54
=36×54
= 1944 cm^2
180= 4× side
180/4 = side
45 cm = side
We know that diagonals of rhombus bisect each other at 90° .
So, diagonal 1 = 72 cm
Half of diagonal 1 =72/2
=36 cm
In ∆AOB
AB^2 = AO^2 + BO^2
45^2 = 36^2 + BO^2
2025= 1296+ BO^2
2025-1296=BO^2
729=BO^2
√729=BO
27 cm =BO
So, Second Diagonal( BD) = 2×BO
=2×27
= 54 cm
Area of rhombus = 1/2 × Diagonal 1 × Diagonal 2
=1/2 ×72 ×54
=36×54
= 1944 cm^2
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