$△ A B C$ is such that $A B = 3 c m, B C = 2 c m$ and $C A = 2.5 c m .$ $△ D E F$ is similar to $△ A B C .$ If $E F = 4 c m$ , then the perimeter of $△ D E F$ is ____.

7.5 cm

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15 cm

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22.5 cm

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30 cm

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Solution

The correct option is B
15 cm

$\frac{A B}{D E} = \frac{A C}{D F} = \frac{B C}{E F} = \frac{2}{4} = \frac{1}{2}$

$D E = 2 \times A B = 6 c m, D F = 2 \times A C = 5 c m$

$∴ Perimeter of Δ D E F$
$= (D E + E F + D F)$
$= 6 + 4 + 5 = 15 c m .$

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Similar questions

$△ A B C$ is such that $A B = 3 c m, B C = 2 c m$ and $C A = 2.5 c m . △ D E F$ is similar to $△ A B C .$ If $E F = 4 c m,$ then the perimeter of $△ D E F$ is

In $△$ ABC, AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ ABC. If EF = 4 cm, then the perimeter of $△$ DEF is -

Q. ∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is

(a) 7.5 cm
(b) 15 cm
(c) 22.5 cm
(d) 30 cm

$△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ ABC. If EF = 4 cm, then the perimeter of $△$ DEF in cm is equal to ___

Triangle $A B C$ is such that $A B = 3 c m, B C = 2 c m$ and $C A = 2.5 c m$ . Triangle $D E F$ is similar to $△ A B C$ . If $E F = 4 c m$ , then the perimeter of $△ D E F$ is:

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△ABC is such that AB=3 cm, BC=2 cm and CA=2.5 cm. △DEF is similar to △ABC. If EF=4 cm, then the perimeter of △DEF is ____.

The correct option is B 15 cm ABDE=ACDF=BCEF=24=12 DE=2×AB=6 cm, DF=2×AC=5 cm ∴Perimeter of ΔDEF =(DE+EF+DF) =6+4+5=15 cm.

$△ A B C$ is such that $A B = 3 c m, B C = 2 c m$ and $C A = 2.5 c m .$ $△ D E F$ is similar to $△ A B C .$ If $E F = 4 c m$ , then the perimeter of $△ D E F$ is ____.

The correct option is B
15 cm

$\frac{A B}{D E} = \frac{A C}{D F} = \frac{B C}{E F} = \frac{2}{4} = \frac{1}{2}$

$D E = 2 \times A B = 6 c m, D F = 2 \times A C = 5 c m$

$∴ Perimeter of Δ D E F$
$= (D E + E F + D F)$
$= 6 + 4 + 5 = 15 c m .$