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Question-208011




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

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