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The ratio of the areas of two triangles is 4:7 . If the areas differ by 36cm^2 find the area of each triangle

Sagot :

[tex] \frac{A_{\triangle1}}{A_{\triangle2}} = \frac{4}{7} \Longrightarrow 4A_{\triangle2}=7A_{\triangle1} \\ A_{\triangle2}-A_{\triangle1}=36~cm^2 \Longrightarrow A_{\triangle2}=A_{\triangle1}+36 \\ Replace: \\ 4(A_{\triangle1}+36)=7A_{\triangle1} \\ 4A_{\triangle1}+144=7A_{\triangle1} \\ 3A_{\triangle1}=144 \\ \boxed{A_{\triangle1}=48~cm^2} \\ A_{\triangle2}=48+36 \\ \boxed{A_{\triangle2}=84~cm^2}[/tex]