SOLUTION: The sum of the radii of two circles is equal to 17 centimeters. The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters. Find the radii

Question 102718: The sum of the radii of two circles is equal to 17 centimeters. The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters. Find the radii.
Hint: Area of a circle= pie*the square of the radius
this quastion makes my head hurt! pls. help!!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x and y equal the two radii ... x+y=17 ... y=17-x ... pi(x^2)+pi(y^2)=pi(13^2) ... x^2+(17-x)^2=13^2

x^2+17^2-34x+x^2=13^2 ... 2x^2-34x+120=0 ... x^2-17x+60=0 ... (x-5)(x-12)=0

x=5 or x=12, so y=12 or y=5 ... the two radii are 5 and 12
RELATED QUESTIONS
Find the area of a circle whose area equals the half of the sum of the areas of two... (answered by htmentor)

The sum of diameters of two circles is 112 cm and the sum of their areas is 5236 cm^2.... (answered by TimothyLamb)

Two circles touch externally.The sum of their areas is 58pi cm^2 and the distance between (answered by lwsshak3)

two circles have diameters which differ by 4.00 cm. if the sum of the areas of the... (answered by mananth)

Calculate the radius of a circle whose area is equal to the sum of the areas of three?... (answered by rapaljer)

The diameter of a circle whose area is equal to the sum of the areas of the two circles... (answered by Theo)

How would you solve the following word problem by setting up two equations? The sum of (answered by edjones)

The sum of radii of two circles is 10.5 cm and the difference of their circumferences is... (answered by TimothyLamb)

Two circles have radii 8 and 11. What is the ratio of the... (answered by Alan3354)