Question

In ∆ABC, MN||BC , MNBC = 130 CM SQUARE. IF AN:NC = 4:5. THEN ∆MAN AREA IS​

Answer 1

Answer:

65

Step-by-step explanation:

1/2 ×130 = 65

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Answer 2

Area of triangle ΔMAN is 32 cm²

Step-by-step explanation:

• Given data

        $\mathbf{\frac{NC}{AN}=\frac{5}{4}}$

        Adding 1 on both side, we get

        $\mathbf{\frac{NC}{AN}+1=\frac{5}{4}+1}$

        $\mathbf{\frac{NC+AN}{AN}=\frac{5+4}{4}}$

        So

        $\mathbf{\frac{AC}{AN}=\frac{9}{4}}$    ...1)

• It is given that MN ║BC. So we can say that $\mathbf{\Delta MAN\sim \Delta ABC}$

• We know that from theorem of ratio of area of similar triangle is equal to ratio of square of corresponding side. Means

        $\mathbf{\frac{ar\Delta ABC}{ar\Delta MAN}=\left ( \frac{AC}{AN} \right )^{2}}$

        $\mathbf{\frac{ar\Delta ABC}{ar\Delta MAN}=\left ( \frac{9}{4} \right )^{2}}$

        $\mathbf{\frac{ar\Delta ABC}{ar\Delta MAN}= \frac{81}{16}}$

• Subtracting 1 on both side, we get

        $\mathbf{\frac{ar\Delta ABC}{ar\Delta MAN}-1= \frac{81}{16}-1}$

        $\mathbf{\frac{ar\Delta ABC-ar\Delta MAN}{ar\Delta MAN}= \frac{81-16}{16}}$

        $\mathbf{\frac{area\ of\ MNBC}{ar\Delta MAN}= \frac{65}{16}}$

• $\mathbf{\frac{130}{ar\Delta MAN}= \frac{65}{16}}$     (Given that area of MNBC =130cm²)

        $\mathbf{\frac{2}{ar\Delta MAN}= \frac{1}{16}}$

        So

        Area of ΔMAN = 32 cm² = This is the answer.