in d given figure,AB=12cm and pt=8cm.if PAxPB=PTsquare(square is only for PT), then write a quadratic equation for finding the length of PA?
To find the length of PA, we can use the given information and apply the Pythagorean theorem in triangle PAB.
In triangle PAB, let the length of PA be x cm.
According to the question, AB = 12 cm and PT = 8 cm.
Using the Pythagorean theorem, we have:
PA^2 + AB^2 = PT^2
Substituting the given values, we get:
x^2 + (12)^2 = (8)^2
Simplifying the equation, we have:
x^2 + 144 = 64
Rearranging the terms, we get:
x^2 = 64 - 144
x^2 = -80
Since we cannot take the square root of a negative number, we conclude that there is no real solution for the length of PA in this scenario.