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Q.

A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+7. If the two adjacent vertices of the rectangle are (−8,5) and (6,5), then the area of the rectangle (in sq. units) is

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a

84

b

98

c

72

d

56

answer is B.

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Detailed Solution

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Let ABCD be the rectangle

Let A=(−8,5)    &  B=(6,5)

Let centre =(−1,α)lies on 3y=x+7

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3α=6

α=2

∴ Centre =(−1,2)

AD=BC=6

AB=14

Area of rectangle =AB×BC=14×6=84

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