Question-199242

Question Number 199242 by Tawa11 last updated on 30/Oct/23

Answered by mr W last updated on 30/Oct/23

Commented by mr W last updated on 30/Oct/23

hatched triangles are similar. (x/2)=(6/( (√(11)))) ⇒x=((12)/( (√(11))))≈3.618

$${hatched}\:{triangles}\:{are}\:{similar}. \\ $$$$\frac{{x}}{\mathrm{2}}=\frac{\mathrm{6}}{\:\sqrt{\mathrm{11}}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{12}}{\:\sqrt{\mathrm{11}}}\approx\mathrm{3}.\mathrm{618} \\ $$

Commented by Tawa11 last updated on 30/Oct/23

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Commented by mr W last updated on 30/Oct/23

$${is}\:{answer}\:{correct}? \\ $$

Commented by AST last updated on 30/Oct/23

Equating the cos of the equal angles will give same answer: (2/X)=((√(11))/6)

$${Equating}\:{the}\:{cos}\:{of}\:{the}\:{equal}\:{angles}\:{will} \\ $$$${give}\:{same}\:{answer}:\:\frac{\mathrm{2}}{{X}}=\frac{\sqrt{\mathrm{11}}}{\mathrm{6}} \\ $$

Commented by mr W last updated on 30/Oct/23

$${yes} \\ $$

Commented by Tawa11 last updated on 31/Oct/23

$$\mathrm{Correct}\:\mathrm{sir}. \\ $$$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$

Answered by cortano12 last updated on 31/Oct/23

by Ptolomeus theorem x(√(x^2 +27)) +18 = (√((x^2 +21)(x^2 +36))) x = ((12(√(11)))/(11))

$$\mathrm{by}\:\mathrm{Ptolomeus}\:\mathrm{theorem}\: \\ $$$$\:\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{27}}\:+\mathrm{18}\:=\:\sqrt{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{21}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{36}\right)} \\ $$$$\:\mathrm{x}\:=\:\frac{\mathrm{12}\sqrt{\mathrm{11}}}{\mathrm{11}} \\ $$

Commented by cortano12 last updated on 31/Oct/23