Answer:
√105
Explanation:
Since line TP is what you are looking for, draw a imaginary line from Point T to Point J, and using Pythagorean Theorem you will find that it is the c² in the
a² + b² = c²
Using Pythagorean Theorem, we can determine the measure of Segment TP by finding the measures of Segments MJ, JP, and the imaginary TJ.
If JK = 24, then half of JK is 12, which is Segment MJ(a²).
If JL = 16, then half of JL is 8, which is segment JP.
Therefore, we can setup a simple mathematical equation where since both MT and TP have right angles, we know that c² will be the imaginary line TJ, since the opposite of the right angle will be the c² always in the Pythagorean Theorem.
Equation:
5² + 12² = c²(or TJ)
8² + TP² = c²(or TJ)
25 + 144 = c²
64 = TP² = c²
Using the Law of Substitution, we can determine that:
25 + 144 = 64 + TP²
169 = 64 + TP²
105 = TP²
TP = √105
That's how I got my answer.
Hope this helps!