# A rectangle with diagonal of length 20cm has sides in the ratio of 2:1 .find the area of the rectangle

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Let the length =2x

and breath = 1x

diagonal = 20cm

20² = (2x)² + (1x)² [ by Pythagoras thm ]

400 = 4x² + 1x²

400 = 5x²

x² = 400/5

x² = 80

x =√80

x = √2×2×2×2×5

x = 4√5

∴length =2x = 2×4√5 = 8√5

breath = 1x= 4√5

∴ area of a rectangle = l×b

= 8√5 × 4√5

=32 ×5

= 160

and breath = 1x

diagonal = 20cm

20² = (2x)² + (1x)² [ by Pythagoras thm ]

400 = 4x² + 1x²

400 = 5x²

x² = 400/5

x² = 80

x =√80

x = √2×2×2×2×5

x = 4√5

∴length =2x = 2×4√5 = 8√5

breath = 1x= 4√5

∴ area of a rectangle = l×b

= 8√5 × 4√5

=32 ×5

= 160