Question

In triangle ABC if f DE is parallel to BC then the value of AD is​

Answer 1

Answer:

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$\large\bf\underline\red{Question ➡} \: \\ \\ \sf \: in \: figure \: if \: DE//BC \: then \: find \: the \: \\ \sf \: value \: of \: AD \\ \\ \large\bf\underline\red{given \: that \: ➡} \\ \\ \bf \bigstar \: \: \: \: DE//BC \\\bf \bigstar \: \: \: \: AE = 1.8 cm \\ </p><p>\bf \bigstar \: \: \: \: EC = 5.4cm \\ \bf \bigstar \: \: \: \: </p><p>DE = 7.2 cm \\ \\ \large\bf\underline\red{solution: ➡} \\ \\ \rm \underline \blue{by \: using \: basic \: proportionality} \\ \:\rm \underline \blue{ theorem : - } \\ \sf \: If \: a \: line \: is \: drawn \: parallel \: to \: one \: \\\sf side \: of \: a \: triangle \: intersecting \: \\ \sf the \: other \: two \: sides \: in \: distinct \: \\ \sf points, \: then \: the \: other \: two \: \\ \sf sides \: are \: divided \: in \: the \\\sf same \: ratio. \\ \\ \bf \underline{therefore : - } \\ \\ \sf \blue{\frac{AD}{DE} = \frac{AE}{EC} } \\ \\ \sf \: \frac{AD}{7.2} = \frac{1.8}{5.4} \\ \\ \sf \underline{by \: cross \: multiplication \: method \: - } \\ \\\sf 5.4 \times AD =1.8 \times 7.2 \\ \\\sf AD \: = \frac{1.8 \times 7.2}{5.4} \\ \\ \sf AD \: = \frac{ \cancel{1.8 }\times 7.2}{ \cancel{5.4} \: ³} \\ \\ \sf \: AD = \frac{7.2}{3} \\ \\ = 2.4 \\ \\ \large\bf \underline{ therefore \: \: AD : - } \\ \large{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{2.4 \: cm}}}}$