In the given figure, if DE/BC=2/3 and AE=10cm, then AB is_______

a) 16cm b) 12cm c) 15cm d) 18cm

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In the given figure, if DE/BC=2/3 and AE=10cm, then AB is_______
a) 16cm b) 12cm c) 15cm d) 18cm

Gursheen kaur. · Accepted Answer

$I n Δ A D E, ∠ A E D = 180^{0} - 105^{0} [a n g l e s u m o f a Δ A E C] ∠ A E D = 75^{0} t h e n I n Δ A B C, ∠ A = 180^{0} - (75^{0} - 65^{0}) = 40^{0} I n Δ A D E, ∠ A D E = 180^{0} - (40^{0} + 75^{0}) = 65^{0} S o, a l l a n g l e s a r e s a m e . I n Δ A D E & Δ A B C, ∠ A E D = ∠ A B C [G i v e n] ∠ D A E = ∠ D A E [C o m m o n] ∴ Δ A D E \sim Δ A B C [E q u i a n g u l a r]$

$\frac{D E}{B C} = \frac{A E}{A B} [C o r r e s p o n d i n g s i d e s i n s i m i l a r t r i a n g l e s] \Rightarrow \frac{2}{3} = \frac{10}{A B} \Rightarrow A B = \frac{10}{2} \times 3 \Rightarrow A B = 15 c m$

In the given figure, if DE/BC=2/3 and AE=10cm, then AB is_______ a) 16cm b) 12cm c) 15cm d) 18cm

In the given figure, if DE/BC=2/3 and AE=10cm, then AB is_______

a) 16cm b) 12cm c) 15cm d) 18cm