SOLUTION: A rectangle is inscribed in a circle of radius 6.5 cm. If the the length of the rectangle is 2 cm longer than twice the width, then the dimensions of the rectangle are:
(A) 4.5
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(A) 4.5
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Question 281414: A rectangle is inscribed in a circle of radius 6.5 cm. If the the length of the rectangle is 2 cm longer than twice the width, then the dimensions of the rectangle are:
(A) 4.5 cm x 11 cm (B) 5 cm x 12 cm (C) 5.5 cm x 13 cm
(D) 6.5 cm x 12 cm (E) none of these
You can put this solution on YOUR website! let the width of the rectangle be x
the length = 2x+2
the radius =6.5 which is half the diagonal. 6.5 *2 =13 will be diagonal
the diagonal is the hypotenuse of the triangle with sides x and 2x +2
x^2+(2x+2)^2=13^2
x^2+4x^2+8x+4=169
5x^2+8x-165=0
5x^2-25x+33x-165=0
5x(x-5)+33(x-5)=0
(x-5)(5x+33)=0
so x = 5 is the width
