Question Number 208011 by necx122 last updated on 02/Jun/24
Commented by necx122 last updated on 02/Jun/24
$${If}\:{the}\:{ratio}\:{of}\:<{ARS}\::\:<{BRT}\:=\:\mathrm{9}:\mathrm{4}, \\ $$$${find}\:{the}\:{ratio}\:{of}\:{area}\:{ABC}\::\:{area}\:{ARS} \\ $$
Commented by A5T last updated on 02/Jun/24
$${Not}\:{unique}. \\ $$
Commented by A5T last updated on 02/Jun/24
Commented by A5T last updated on 02/Jun/24
$${Do}\:{you}\:{mean}\:{angle}\:\angle\:?\:{or}\:{area}? \\ $$
Commented by mr W last updated on 02/Jun/24
$${queation}\:{is}\:{badly}\:{written}.\:{i}\:{think}\: \\ $$$${he}\:{means}\:{the}\:{ratio}\:{of}\:{areas},\:{not}\:{the} \\ $$$${ratio}\:{of}\:{angles}. \\ $$
Commented by necx122 last updated on 03/Jun/24
$${unfortunately}\:{I}\:{didnt}\:{make}\:{a}\:{mistake}. \\ $$$${Based}\:{on}\:{my}\:{reference}\:{text}\:{they}\:{wrote} \\ $$$${the}\:{symbol}\:{for}\:{angle}\:{and}\:{not}\:{area}.\:{I}\:{can} \\ $$$${see}\:{now}\:{that}\:{the}\:{issue}\:{came}\:{from}\:{the} \\ $$$${textbook}.\:{Thanks} \\ $$
Answered by mr W last updated on 02/Jun/24
Commented by mr W last updated on 02/Jun/24
$$\frac{\Delta{ARS}}{\Delta{BRT}}=\frac{\mathrm{9}}{\mathrm{4}}=\left(\frac{{a}}{{b}}\right)^{\mathrm{2}} \:\Rightarrow\frac{{a}}{{b}}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\frac{\Delta{ABC}}{\Delta{ARS}}=\left(\frac{{b}+{a}}{{a}}\right)^{\mathrm{2}} =\left(\mathrm{1}+\frac{{b}}{{a}}\right)^{\mathrm{2}} =\left(\mathrm{1}+\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{25}}{\mathrm{9}} \\ $$
Commented by necx122 last updated on 02/Jun/24
$${This}\:{is}\:{wonderful}\:{for}\:{real}. \\ $$
Commented by Tawa11 last updated on 21/Jun/24
$$\mathrm{Weldone}\:\mathrm{sir} \\ $$