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Byju's Answer

Standard VIII

Mathematics

Dilations

In a Δ ABC,...

Question

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = 8 c m, A B = 12$ and $A E = 12 c m$ , find $C E$ .

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Solution

$\begin{matrix} D B = A B - A D = 12 - 8 = 4 c m I n Δ A D E & Δ A B C ∠ A = ∠ A & ∠ A D E = ∠ A B C ∴ Δ A D E \sim Δ A B C \frac{A D}{A B} = \frac{A E}{A C} \Rightarrow \frac{8}{12} = \frac{12}{12 + x} 96 + 8 x = 144 8 x = 144 - 96 ∴ x = \frac{48}{8} = 6 c m . \end{matrix}$

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Similar questions

D

and

E

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A B

and

A C

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A B = 12 c m, A D = 8 c m, A E = 12 c m

and

A C = 18 c m

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D E ∥ B C

Q. In a

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Δ A B C

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and

E

are points on the sides

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respectively such that

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D and E are the points on the sides AB and AC respectively of a $Δ A B C$ such that: AD = 8 cm, DB =12 cm, AE = 6cm and CE = 9 cm. Prove that $B C = \frac{5}{2} D E$ .

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Δ A B C

D

and

E

are points on the sides

A B

and

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In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.If AD=8 cm,AB=12 and AE=12 cm, find CE.

DB=AB−AD=12−8=4cmInΔADE&ΔABC∠A=∠A&∠ADE=∠ABC∴ΔADE∼ΔABCADAB=AEAC⇒812=1212+x96+8x=1448x=144−96∴x=488=6cm.

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = 8 c m, A B = 12$ and $A E = 12 c m$ , find $C E$ .

$\begin{matrix} D B = A B - A D = 12 - 8 = 4 c m I n Δ A D E & Δ A B C ∠ A = ∠ A & ∠ A D E = ∠ A B C ∴ Δ A D E \sim Δ A B C \frac{A D}{A B} = \frac{A E}{A C} \Rightarrow \frac{8}{12} = \frac{12}{12 + x} 96 + 8 x = 144 8 x = 144 - 96 ∴ x = \frac{48}{8} = 6 c m . \end{matrix}$