Use pythagorean identities to prove whether δlmn is a right, acute, or obtuse triangle. show all work for full credit.

Using Pythagorean identities:
 
If the sum of the height and base squared is greater than the hypotenuse squared, it would be an acute triangle.

If the sum of the height and base squared is less than the hypotenuse squared, it would be an obtuse triangle.

If the sum of the height and base squared is equal to the hypotenuse squared, it would be a right triangle.

The height = 10
The base = 24

10^2 + 24^2 = 100 + 576 = 676

The hypotenuse = 27 = 27^2 = 729

Because the sum of the height and base squared (676) is smaller than the hypotenuse squared (729) the triangle  is an obtuse triangle.