Question

if∆abc~∆def such that 3ab =de and bc =9 then find ef​

Answer 1

Answer:

27 units

Step-by-step explanation:

ΔABC ~ ΔDEF

3 AB = DE

⇒$\frac{AB}{DE} \\\\=\frac{1}{3}$

by CPST, AB / DE = BC / EF

⇒ 1/3 = 9 / EF

Cross multiply

EF = 9 × 3 = 27

Answer 2

Answer:

The value of EF is 27 cm.

Step-by-step explanation:

Given:-

ΔABC is similar to ΔDEF such that 3AB = DE and BC = 9 cm.

To find:-

The value of EF.

Step 1 of 1

According to the question,

ΔABC is similar to ΔDEF, i.e.,

∆ABD ≈ ∆DEF

Then,

∠$A$ = ∠D, ∠$B$ = ∠E and ∠$C$ = ∠F.

It is also given that 3AB = DE.

⇒ AB/DE = 1/3 . . . . (1)

Using the property of similar triangles, we have

$\frac{AB}{BC}=\frac{DE}{EF}$

or,

$\frac{AB}{DE}=\frac{BC}{EF}$

From (1), we get

$\frac{1}{3}=\frac{BC}{EF}$

$\frac{1}{3}=\frac{9}{EF}$ (Given, BC = 9 cm)

Cross multiply the equation as follows:

⇒ EF = 3 × 9

⇒ EF = 27 cm.

Therefore, the value of EF is 27 cm.

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