In $Δ A B C \sim Δ D E F$ and their areas are ${36 c m}^{2}$ and ${64 c m}^{2}$ respectively.If side AB=3 cm. Find DE.

3 cm

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2 cm

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5 cm

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4 cm

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Solution

The correct option is D 4 cm
In $Δ A B C \sim Δ D E F$
$\frac{a r . (Δ A B C)}{a r . (Δ D E F)} = \frac{{A B}^{2}}{{D E}^{2}} = \frac{{A C}^{2}}{{D F}^{2}} = \frac{{B C}^{2}}{{E F}^{2}}$
$\frac{36}{64} = \frac{{A B}^{2}}{{D E}^{2}}$
$\frac{6}{8} = \frac{3}{D E}$
$D E = \frac{8 \times 3}{6} = \frac{24}{6} = 4 c m$
Therefore, D is the correct answer.

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Similar questions

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 $Δ D E F$ .

Q. Question 1
Let

Δ A B C \sim Δ D E F

and their areas be, respectively,

64 c m^{2}

and

121 c m^{2}

. If EF = 15.4 cm, find BC.

Q. Triangles ABC and DEF are similar.

(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF.
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm , find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² 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 ∆ABC and ∆DEF.

If $Δ A B C \sim Δ D E F$ such that $A B = 1.2$ cm and
$D E = 1.4$ cm. Find the ratio of of areas of $Δ A B C$ and $Δ D E F$

$Δ A B C \sim Δ D E F$ and their areas are respectively 64 $c m^{2}$ and 121 $c m^{2}$ . If EF = 15.4 cm, find BC.

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In ΔABC∼ΔDEF and their areas are 36cm2 and 64cm2 respectively.If side AB=3 cm. Find DE.

The correct option is D 4 cmIn ΔABC∼ΔDEFar.(ΔABC)ar.(ΔDEF)=AB2DE2=AC2DF2=BC2EF23664=AB2DE268=3DEDE=8×36=246=4cmTherefore, D is the correct answer.

In $Δ A B C \sim Δ D E F$ and their areas are ${36 c m}^{2}$ and ${64 c m}^{2}$ respectively.If side AB=3 cm. Find DE.