Open Middle®
Directions: Using the digits 0 to 9 at most one time each, create two similar triangles. You may have as many leading zeros as you like.
Hint
Can you use a scale factor to help you in any way?
What is true about the corresponding sides of similar triangles?
What is true about the corresponding sides of similar triangles?
Answer
There are many answers. Here are the possibilities:
YA – 5
AH – 10
YB – 3
BV – 6
BA – 9
VH – 27
YA – 5
AH – 10
YB – 3
BV – 6
BA – 9
VH – 27
Source: Drew Ross
In your solution the sides of your smaller triangle are 3, 5, and 9. There is no such possible triangle as the sun of any two sides of a triangle must be greater than the third. 3 + 5 = 8, thus you cannot have a 3,5,9 triangle. The larger triangle is also impossible since it is a dilation of the smaller figure.
Here’s one solution I found…
YA – 4
AH – 8
YB – 5
BV – 10
BA – 3
VH – 9
The solution provided does not follow the triangle inequality so they won’t actually form a triangle.
Another solution would be:
AY: 6
AH: 18
AB: 5
HV: 20
YB: 3
BV: 9