In the adjoining figure- DE- BC If ADDB-35 and AC-9-6cm- find AE-

The correct option is C 3.6cm Since DE∥ BC , we have ADDB=AEEC ∴ AEEC=35 [ ∵ AD EC = 3 5 ]Let AE=xcm . Then EC=(AC ...

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Standard IX

Mathematics

The Mid-Point Theorem

In the adjoin...

Question

In the adjoining figure, $D E ∥ B C$ If $\frac{A D}{D B} = \frac{3}{5}$ and $A C = 9.6 c m$ , find $A E$ .

3.8 c m

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7.2 c m

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3.6 c m

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4.5 c m

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Solution

The correct option is C $3.6 c m$
Since $D E ∥ B C$ , we have $\frac{A D}{D B} = \frac{A E}{E C}$
$∴$ $\frac{A E}{E C} = \frac{3}{5}$ [ $∵ \frac{A D}{E C} = \frac{3}{5}$ ]
Let $A E = x c m$ . Then $E C = (A C - A E) = (9.6 - x) c m$
$∴$ $\frac{x}{9.6 - x} = \frac{3}{5} \Rightarrow 5 x = 3 (9.6 - x)$
$\Rightarrow 5 x = 28.8 - 3 x$ $\Rightarrow 8 x = 28.8$ $\Rightarrow x = 3.6$
$∴$ $A E = 3.6 c m$

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Similar questions

In the adjoining figure, DE || BC.
(i) If AD=3.4 cm, AB=8.5 cm and AC=13.5 cm, find AE.
(ii) If $\frac{A D}{D B} = \frac{3}{5}$ and AC=9.6 cm, find AE.

In the adjoining figure, AD=5.6 cm, AB=8.4cm, AE=3.8cm and AC=5.7cm. Show that DE||BC.

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In the adjoining figure, DE∥BC If ADDB=35 and AC=9.6cm, find AE.

The correct option is C 3.6cmSince DE∥BC, we have ADDB=AEEC∴ AEEC=35 [∵ADEC=35]Let AE=xcm. Then EC=(AC−AE)=(9.6−x)cm∴ x9.6−x=35⇒5x=3(9.6−x)⇒5x=28.8−3x ⇒8x=28.8 ⇒x=3.6∴ AE=3.6cm

In the adjoining figure, $D E ∥ B C$ If $\frac{A D}{D B} = \frac{3}{5}$ and $A C = 9.6 c m$ , find $A E$ .