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The Mid-Point Theorem

In the adjoin...

Question

In the adjoining figure, $D E ∥ B C$ If $A D = 3.4 c m, A B = 8.5 c m$ and $A C = 13.5 c m$ , find $A E$ .

2.4 c m

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3.4 c m

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2.1 c m

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5.4 c m

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Solution

The correct option is D $5.4 c m$
Since $D E ∥ B C$ , from Basic Proportionality Theorem,
we have $\frac{A D}{A B} = \frac{A E}{A C}$
$∴$ $\frac{3.4}{8.5} = \frac{A E}{13.5} \Rightarrow \frac{3.4 \times 13.5}{8.5} = 5.4$
Hence, $A E = 5.4 c m$

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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.

Q. In

△ A B C, D E ∥ B C

, point

D

lies

A B

and

E

lies on

A C

. If

A D = 3.4 c m, A B = 10 c m, A E = 5.1 c m

then find the value of

A C

Q. In the given figure,

D E ∥ B C

. If

A D = 3.6 c m, A B = 9 c m

and

A E = 2.4 c m

, find

E C

Q. In a

△ A B C, D

and

E

are points on the sides

A B

and

A C

respectively such that

D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E = 2 c m

and

B C = 5 c m

, find

B D

and

C E

Q. In the adjoining figure,

D E ∥ B C

\frac{A D}{D B} = \frac{3}{5}

and

A C = 9.6 c m

, find

A E

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In the adjoining figure, DE∥BC If AD=3.4cm,AB=8.5cm and AC=13.5cm, find AE.

The correct option is D 5.4cmSince DE∥BC, from Basic Proportionality Theorem, we have ADAB=AEAC∴ 3.48.5=AE13.5⇒3.4×13.58.5=5.4Hence, AE=5.4cm

In the adjoining figure, $D E ∥ B C$ If $A D = 3.4 c m, A B = 8.5 c m$ and $A C = 13.5 c m$ , find $A E$ .

The correct option is D $5.4 c m$
Since $D E ∥ B C$ , from Basic Proportionality Theorem,
we have $\frac{A D}{A B} = \frac{A E}{A C}$
$∴$ $\frac{3.4}{8.5} = \frac{A E}{13.5} \Rightarrow \frac{3.4 \times 13.5}{8.5} = 5.4$
Hence, $A E = 5.4 c m$