Question

△ABC has measurements AB = 15 cm, BC = x cm, and AC = 32 cm. If BC is the longest side of the triangle, what are the possible values for x that guarantee △ABC is an obtuse triangle?

Answer 1

For △ABC to be an obtuse triangle with BC being the longest side, x (the length of BC) must be greater than the square root of the sum of squares of the other two sides, meaning x must be greater than approximately 35.35 cm.

Step-by-step explanation:

To determine the possible values for x that guarantee △ABC is an obtuse triangle where BC is the longest side, we use the property that in an obtuse triangle, the square of the longest side is greater than the sum of the squares of the other two sides. Given AB = 15 cm and AC = 32 cm, the condition for △ABC to be obtuse is:

x^2 > AB^2 + AC^2
x^2 > 15^2 + 32^2
x^2 > 225 + 1024
x^2 > 1249

Therefore, x must be greater than the square root of 1249. Calculating the square root gives us:

√1249 ≈ 35.35 cm

So, the length of BC (x) must be greater than 35.35 cm to ensure that △ABC is an obtuse triangle.