- DEF - MNK- If DE-2- MN-5- then find the value of Area- DEFAreaMNK

If we know that Δ DEF ∼Δ MNK Then DEMN = EFNK = FDKM = √(Area(Δ DEF)Area(Δ MNK)) It is given that DE = 2, MN = 5 Therefore, DEMN =√(Area ...

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Standard X

Mathematics

Similar Triangles

Δ DEF ∼Δ MNK....

Question

$Δ D E F \sim Δ M N K$ . If $D E = 2, M N = 5$ , then find the value of $\frac{A r e a (Δ D E F)}{A r e a (M N K)}$

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Solution

If we know that $Δ D E F \sim Δ M N K$
Then $\frac{D E}{M N} = \frac{E F}{N K} = \frac{F D}{K M} =$ $\sqrt{\frac{A r e a (Δ D E F)}{A r e a (Δ M N K)}}$

It is given that $D E = 2, M N = 5$
Therefore,
$\frac{D E}{M N} = \sqrt{\frac{A r e a (Δ D E F)}{A r e a (Δ M N K)}} = \frac{2}{5}$
$\Rightarrow \frac{A r e a (Δ D E F)}{A r e a (Δ M N K)} = (\frac{2}{5})^{2} = \frac{4}{25}$

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Δ

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= 5

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Trinagles ABC and DEF are similar.
(i) If area $(Δ A B C) = 16 c m^{2}, a r e a (Δ D E F) = 25 c m^{2}$ and BC = 2.3 cm find EF.
(ii) If area $(Δ A B C) = 9 c m^{2}, a r e a (Δ D E F) = 64 c m^{2}$ and DE=5.1 cm, find AB.
(iii) If AC = 19 cm adn DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area $(Δ A B C) = 36 c m^{2}$ , are $(Δ D E F) = 64 c m^{2}$ and DE= 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE=1.4 cm, find the ratio of the areas of $Δ A B C$ and $Δ D E F$ .

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ΔDEF∼ΔMNK. If DE=2,MN=5, then find the value of Area(ΔDEF)Area(MNK)

If we know that ΔDEF∼ΔMNKThen DEMN=EFNK=FDKM=√Area(ΔDEF)Area(ΔMNK)It is given that DE=2,MN=5Therefore,DEMN=√Area(ΔDEF)Area(ΔMNK)=25⇒Area(ΔDEF)Area(ΔMNK)=(25)2=425

$Δ D E F \sim Δ M N K$ . If $D E = 2, M N = 5$ , then find the value of $\frac{A r e a (Δ D E F)}{A r e a (M N K)}$