Question

If. ∆ABC~PQR and AB:PQ=2:3 then the ratio of area of them is.....​

Answer 1

Answer:

$\large\bf\underline\red{Question ➡} \\ \sf \: if \: ∆ABC \: similar \: ∆PQR \: and \: \\\sf AB:PQ \: = 2:3 \: then \: the \: ratio \: of \: \\\sf \: their area \: is \: ? \\ \\ \large\bf\underline\red{given \: that \: ➡} \\ \\\bf✫ \: ∆ABC \: similar \: ∆PQR \\ \bf✫ \: AB:PQ \: = 2:3 \\ \\ \large\bf\underline\red{solution➡} \\ \\\sf\blue{we \: know \: that \: the \:ratio \: of \: the \: areas \: } \\ \sf\blue{of \: two \: similar \: triangle \:is \: equal \: to \: } \\ \sf\blue{the \: ratios \: of \: the \: squares \: } \\\sf\blue { of \:any \: two \: corresponding \:sides } \\ \\ \small\bf\underline\red{therefore ➡} \\ \\ \sf \frac{ar( ∆ABC)}{ar(∆PQR)} = \frac{ {(AB)}^{2} }{ {(PQ)}^{2} } \\ \\ ➡ \sf \frac{ar( ∆ABC)}{ar(∆PQR)} = \frac{ {(2)}^{2} }{ {(3)}^{2} } \\ \\ ➡ \sf \frac{ar( ∆ABC)}{ar(∆PQR)} = \large{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{4/9}}}}$

ratio of their areas➡

∆ABC:∆PQR = 4:9