Question

find the unknown length X in the following figures

Answer 1

i hope that this is right answer

Answer 2

Answer:

$\red { Value \: of \: X } \green{=4\:m + 3\sqrt{15}}$

Step-by-step explanation:

$In \: \triangle ABC \: AB = 5 \:m , AC = 12\:m \\AD = 3 \:m\:and \: BC = X \: m$

$i) In \: \triangle ABD , \angle ADB = 90\degree$

$\blue { AB^{2} = BD^{2} + AD^{2} }$

$\orange { ( By \: Phythagorean \: theorem )}$

$\implies 5^{2} = BD^{2} + 3^{2}$

$\implies 25 - 9 = BD^{2}$

$\implies BD = \sqrt{16} = 4\:m \:---(1)$

$ii) In \: \triangle ADC , \angle ADC = 90\degree$

$\blue { AC^{2} = DC^{2} + AD^{2} }$

$\orange { ( By \: Phythagorean \: theorem )}$

$\implies 12^{2} = DC^{2} + 3^{2}$

$\implies 144 - 9 = DC^{2}$

$\implies DC = \sqrt{135}\\= \sqrt{9\times 15}\\ = 3\sqrt{15}\:m \:---(2)$

Therefore.,

$\red { Value \: of \: X } = BD + DC\\=4\:m + 3\sqrt{15}$

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