Question

Can a triangle be made from the lengths 5m, 7m, and 9m? If so what kind of triangle; acute, obtuse, or right?

Answer 1

Obtuse.

Explanation:

Yes a triangle can be made as 7 + 5 > 9.

Test for an acute triangle:

For acute triangle c^2 < a^2 + b^2 where c is the longest side.

For right triangle c^2 = a^2 + b^2 where c is the longest side.

For obtuse triangle c^2 > a^2 + b^2 where c is the longest side.

Here:

9 ^2 = 81 = c^2

5^2 + 7^2 = 25 + 49 = 74 = a^2 + b^2.

- so the triangle is not acute.

Here c^2 > a^2 + b^2 therefore the triangle is Obtuse.