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
Algebra.Com
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
Answer by mananth(16946) (Show Source): 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
length is 2x+2 =12
RELATED QUESTIONS
The length of a rectangle is 5 cm longer than twice the width. If the width of the... (answered by algebrahouse.com)
The length of a rectangle is 3 cm longer than twice its breadth. If the perimeter of the... (answered by greenestamps)
The length of a rectangle is 1 cm shorter than the diagonal. The length is 2 cm longer... (answered by Boreal)
The length of a rectangle is 2 cm longer than its width. If the diagonal of the rectangle (answered by jorel1380)
The length of a rectangle is 2 cm more than twice its width. If the perimeter of the... (answered by ewatrrr)
A rectangle is 8 cm longer than it is wide. Find the dimensions of the rectangle if its... (answered by Grinnell,mananth)
The length of a rectangle is 5 cm longer than the width. The perimeter of the rectangle... (answered by JulietG,josgarithmetic)
The length of a rectangle is 2cm longer than twice its width. If the perimeter of the
(answered by josgarithmetic)
The length of a rectangle is 2 cm more than twice its width. If the perimeter of the... (answered by aaaaaaaa)