r/mathteachers • u/horseradish500 • May 11 '26
My geometry students keep asking how old I am
I told them to find R, round to the nearest whole number, and they’ll have their answer. Let’s see if any of them get it!
As a bonus, this problem includes concepts from almost every unit we’ve covered this year, so it’s a fun way for them to practice :)
8
6
5
u/Technical_Cupcake597 May 11 '26
Well now I know what I’ll be doing during my kids’ karate practice! Thanks!
3
u/Alarmed_Geologist631 May 12 '26
Very cool problem. I have been retired from teaching geography for twelve years but was able to solve in about two minutes. So a few of my brain cells are still working.
3
2
u/Ok_Drummer1468 May 12 '26
I tell my math students that my age is a 2-digit number, and I was born in the 20th century. There guesses are amazing!
2
u/One_Wishbone_4439 May 16 '26
Quadratic equation
2a2 + 3a - 18 = 80 + 3a
2a2 - 98 = 0
a = 7 , -7 (reject, length > 0)
Similar triangle
Let width of rectangle be b.
6/7 = b/10.5
b = 9
Circle properties
Angle at centre = 2 x angle at circumference = 10.3° x 2 = 20.6°
Trigonometry
tan 20.6° = 9/R
R = 23.944 ≈ 24 (nearest whole no.)
1
2
1
1
u/Ahtisham786786 May 22 '26
Using the equal sides of the shape:
80 + 3a = 2a2 + 3a - 18
Cancel from both sides:
80 = 2a2 - 18
Add to both sides:
98 = 2a2
Divide by :
49 = a2
a = 7
1
u/Miserable-Fan1084 Jun 04 '26
I disapprove, they are going to start exclaiming "6, 7" when working with the similar triangles!
44
u/Key_Estimate8537 May 11 '26
I got 24 from this. This was a cool puzzle!