book Maths Puzzle Numerical Ability

The vertices of a right triangle are (-12,8), (24,8), and (24,-7). Find the lenght of the hypotenuse of the triangle.

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book Other Question

Prove that a linear operator T on a finite-dimensional vector space is invertible if and only if zero is not an eigenvalue of T. i am supposed to find a value of "x", but i am not given the equation, only its derrivative. and when i integrate it, i get a value plus a constant, which i do not know. pls help