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Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

In Fig. 7.256...

Question

In Fig. 7.256, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.

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Solution

In ∆ABC, DE || BC.

Using basic proportionality theorem, we have

$\frac{AD}{BD} = \frac{AE}{CE} \Rightarrow \frac{AD}{7.2 cm} = \frac{1.8 cm}{5.4 cm} \Rightarrow AD = \frac{1.8 \times 7.2}{5.4} = 2.4 cm$

Thus, the length of the side AD is 2.4 cm.

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Similar questions

In a $Δ A B C$ , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12cm, AD = 8 cm, AE = 12 cm and AC= 18cm.
(ii)AB = 5.6cm, AD= 1.4cm, AC = 7.2 cm and AE= 1.8 cm.
(iii) AB= 10.8 cm, BD= 4.5cm, AC = 4.8cm and AE =2.8 cm.
(iv)AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and EC = 5.5 cm.

Q. In given figure

D

and

E

are respectively the points on the sides

A B

and

A C

of a

△ A B C

such that

A B = 5.6 c m, A D = 1.4 c m, A C = 7.2 c m

and

A E = 1.8 c m

. Then show that

D E | | B C

Q. In Fig.,

D

and

E

are points on side

B C

of a

△ A B C

such that

B D = C E

and

A D = A E

. Show that

△ A B D ≅ △ A C E

Q. In ∆ABC, DE ∥ BC so that AD = 2.4 cm, AE = 3.2 cm and EC = 4.8 cm. Then, AB = ?

(a) 3.6 cm
(b) 6 cm
(c) 6.4 cm
(d) 7.2 cm

D and E are respectively the points on the sides AB and AC of a $Δ$ ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, prove that DE || BC.

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In Fig. 7.256, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.

In ∆ABC, DE || BC. Using basic proportionality theorem, we have ADBD=AECE⇒AD7.2 cm=1.8 cm5.4 cm⇒AD=1.8 × 7.25.4=2.4 cm Thus, the length of the side AD is 2.4 cm.

In ∆ABC, DE || BC.

Using basic proportionality theorem, we have

$\frac{AD}{BD} = \frac{AE}{CE} \Rightarrow \frac{AD}{7.2 cm} = \frac{1.8 cm}{5.4 cm} \Rightarrow AD = \frac{1.8 \times 7.2}{5.4} = 2.4 cm$

Thus, the length of the side AD is 2.4 cm.