1.

Rectangle ABCD has area 200 sq. unit.An ellipse with area 200pi sq.unit passes through Aand C has focii at B and D. Then perimeter of the rectangle ABCD is

Answer»

80 UNIT
40 unit
20 unit
60 unit

Solution :
Area of ellipse `piab=200pi`
`rArr` AB=200 …(1)
Given AB x AD =200 …(2)
AB+AD=2A
Squaring bothsides
`AB^2+AD^2 +2AB xx AD =4A^2`
`BD^2 + 2 xx 200 = 4a^2`
`4a^2e^2 + 400 =4a^2`
`100=a^2 - a^2e^2`
`100=b^2`
`rArr` b=100
`therefore` ab=200
a=20
Perimeter of rectangle ABCD=2 (AB+AD)
=2 x 2a
=4a
= 4 x 20 =80


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