Let ∆ABC~∆DEF and their areas be, respectively, 64cm² and 121cm². If EF= 15.4cm,find BC.

Let ∆ABC~∆DEF and their areas be, respectively, 64cm² and 121cm²

1.	Let ∆ABC~∆DEF and their areas be, respectively, 64cm² and 121cm². If EF= 15.4cm,find BC.
Answer» {tex}\\vartriangle {/tex} ABC {tex} \\sim {/tex}{tex}\\vartriangle {/tex}\xa0DEF ...............Given{tex}\\therefore {/tex}{tex}{{ar(\\Delta ABC)} \\over {ar(\\Delta DEF)}} = {\\left( {{{BC} \\over {EF}}} \\right)^2}{/tex} ..........[The ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides]{tex}\\Rightarrow {/tex}{tex}\\frac{{64}}{{121}} = {\\left( {\\frac{{BC}}{{15.4}}} \\right)^2} \\Rightarrow {\\left( {\\frac{8}{{11}}} \\right)^2} = {\\left( {\\frac{{BC}}{{15.4}}} \\right)^2}{/tex}{tex}\\Rightarrow {/tex}{tex}\\frac{8}{{11}} = \\frac{{BC}}{{15.4}}{/tex} ...........Taking square root on both sides{tex}\\Rightarrow {/tex} BC={tex}\\frac{{8 \\times 15.4}}{{11}} \\Rightarrow BC = 11.2\\,cm{/tex}