Answer:
x = 44.5
Step-by-step explanation:
Two sides of the given triangle have same length.
-> It is an isosceles triangle.
Perpendicular dropped from the vertex to the non-congruent side of an isosceles triangle bisects the side.
By Pythagoras Theorem:
[tex] {(9)}^{2} + \bigg( \frac{x}{2} \bigg) = {(24)}^{2} \\ \\ \implies \: 81 + \frac{ {x}^{2} }{4} = 576 \\ \\ \implies \: \frac{ {x}^{2} }{4} = 576 - 81\\ \\ \implies \: \frac{ {x}^{2} }{4} = 495\\ \\ \implies \: \frac{ {x}^{2} }{4} = 495 \times 4\\ \\ \implies \: { {x}^{2} }= 1980 \\ \\ \implies \: x = \pm \sqrt{1980} \\ \\ \implies \: x \pm \: 44.4971909 \\ \\ \implies \: x = \pm \: 44.5 \\ x \: can \: not \: be \: negative \\ \implies \: x = \: 44.5 [/tex]
