Question

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
(A) 72 (B) 84
(C) 98 (D) 56

Answer 1

Given:  line 3y = x + 7 , two adjacent vertices of the rectangle are (–8, 5) and (6, 5)

To find: area of the rectangle (in sq. units)

Solution:

• So, in a circle as AB is horizontal, let say, A(-8,5), B(6,5), C(6,b) and D(-8,a),

• Here, x coordinate of C is 6 because it lies above the point B,

• Similar goes for point D.

• So, to calculate mid point of AC, we have the formula

                {  (x1 + x2)/2, (y1 + y2)/2  }

• The mid point of AC is

                {  -8+6/2 , 5+b/2  }

                {   -1, 5+b/2  }

• Since they have given that this point should lie on diameter so,

• Putting these points in equation given,

• We get:

               3(5+b)/2 = -1 + 7

               5+b/2 = 2

               5+b=4

               b=-1

• so, the point C is (6,-1).

• So the area of rectangle is :

                AB X BC

                (6-(-8)) X (5-(-1))

                14 X 6

                84 sq. units

Answer:

        The area of the rectangle (in sq. units) is (B) 84 sq. units