SOLUTION: This problem is from a problem solving worksheet known as "Math Olympiads" It is labeled "Problems-Division E Olympiads" The title at the top of the page is "Set 3 Olympiad 1"

Question 166932: This problem is from a problem solving worksheet known as "Math Olympiads"
It is labeled "Problems-Division E Olympiads" The title at the top of the page is "Set 3 Olympiad 1"
A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the reast of the triangle. What is the area of the complete triangle, in sq cm?
Please help us! This is our 5th grade son's homework. We are both college educated and my husband even has a math minor. This is not our finest moment.
Thank You!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the rest of the triangle. What is the area of the complete triangle, in sq cm?
:
Let A = triangle area
then
3A = circle area
and
let x = the common area that is removed
:
from the statement we can write an equation:
3A - x = A - x + 14
Add x to both sides and find A
3A - A = 14
2A = 14
A = 7 sq/cm is the area of the triangle
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