Question

Find the value of x. Write your answer as a decimal rounded to the nearest tenth.

Answer 1

x = 44.5

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:

`{(9)}^(2) + \bigg( (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 * 4\\ \\ \implies \: { {x}^(2) }= 1980 \\ \\ \implies \: x = \pm √(1980) \\ \\ \implies \: x \pm \: 44.4971909 \\ \\ \implies \: x = \pm \: 44.5 \\ x \: can \: not \: be \: negative \\ \implies \: x = \: 44.5`