Question

The perimeter of a triangle is between 10 and 15 inclusively if two of the sides of the triangle are 3.7 and 5.2 find the range of possible measurements of the third side

Answer 1

Explanation:

Triangle side length rule says the sum of any two sides must be greater than the third side....let 'x' be the missing side, then:

3.7 + x > 5.2 so x > 1.5

3.7 + 5.2 > x x < 8.9

5.2 + x > 3.7 true already

so without any constraints:

1.5< x < 8.9 BUT there is a constraint....the perimeter is <= 15

so x + 8.9 <= 15

shows x <=6.1

then the range becomes a bit restricted to:

1.5 < x <= 6.1 ( the other constraint is already met as

8.9 + 1.5 is greater than 10 )