Question

A rectangle is inscribed in a circle with a perimeter lying along the line 3y = x+7. If the two adjacement verticles of the rectangle are (-8, 5) and (6,5), then the area of the rectangle ( in sq units) is
A. 72
B. 84
C. 98
D. 56

Answer 1

Correct Answer - B
Given points are (-8 , 5) and (6, 5) in which y- coordinate is same , i.e., these points lie on horizontal line y = 5.

Let `(-8, beta) and (6, beta)` are the coordinates of the other vertices of rectangle as shown in the figure.
Since, the mid-point of line joining points (-8, 5) and `(6, beta)` lies on the line 2y = x + 7.
`therefore 3((5+beta)/(2))=(-8+6)/(2)+7`
`rArr 15 + beta=-2+14`
`rArr 3beta=-3rArrbeta = -1`
Now, area of rectangle `=|-8-6|xx|beta-5|`
`=14+6=84`