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# Area of Three Triangles

Directions: Use the integers 2 through 10, at most one time each, as lengths of individual sides to form three triangles. What is the smallest total area of the three triangles you can create? What is the largest?

### Hint

For Geometry: You will need to give them Heron’s formula if they don’t know it.
For Trig: “How can we find the area of a triangle if we know all three sides but no angles?”
In general: “How can I make sure all three are triangles?”

### Answer

Minimum Area: 2-9-10, 3-6-7 and 4-5-8
Maximum Area: 2-3-4, 5-6-7, 8-9-10

Source: Dan Wulf

## Pythagorean Inequality

Directions: Using the digits 1 through 6 at most one time each, fill in the …

### 2 comments

1. Why do you have multiple “minimum” area answers? And multiple “maximum”?

And why was 2, 3, 4 included…

These answers don’t make sense to me, am I missing something?

• I am reading the answers as the measurements of the three sides. We need to find three sets of three numbers. 2, 3, 4 are valid from the question