Answer: Lukas is incorrect. The side lengths do not satisfy the triangle inequality rule so no triangles can be drawn given these side lengths.
Step-by-step explanation:
Here is the complete question
Lukas wants to create a triangle with sides measuring 9 in., 13 in., and 15 in. He says that more than one triangle is possible given these side lengths. Which statement about Lukas’s claim is true?
A. Lukas is incorrect. The side lengths satisfy the triangle inequality rule so one unique triangle can be drawn.
B. Lukas is incorrect. The side lengths do not satisfy the triangle inequality rule so no triangles can be drawn given these side lengths.
C. Lukas is correct. The side lengths satisfy the triangle inequality rule so multiple triangles can be drawn.
D. Lukas is correct. The side lengths do not satisfy the triangle inequality rule so multiple triangles can be drawn.
For the figures to make up a triangle, the addition of the square of the two smaller sides must be equal to the square of the larger side. The Pythagoras rule is used.
The figures here are 9, 13 and 15. So let's yes to confirm.
9^2 + 13^2 = 15^2
81 + 169 = 225
250 = 225
Since the two figures are not equal, it is incorrect no triangles can be drawn from the length.
