Triangles ABC and DEF are similar. If their areas are 64 $c m^{2}$ and 49 $c m^{2}$ and if AB is 7 cm, then find the value of DE.

8 cm

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\frac{49}{8}

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\frac{8}{49}

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\frac{64}{7}

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Solution

The correct option is C $\frac{49}{8}$ cm
$Δ A B C Δ D E F$
$\frac{A B}{D E} = \frac{B C}{E F} = \frac{A C}{D F}$ .
We know that,
$\frac{A r e a o f Δ A B C}{A r e a o f Δ D E F} =$ $\Rightarrow \frac{64}{49} = {(\frac{7}{D E})}^{2}$
$\Rightarrow {(\frac{8}{7})}^{2} = {(\frac{7}{D E})}^{2} \Rightarrow {(\frac{8}{7})}^{2} = {(\frac{7}{D E})}^{2} = \frac{49}{8}$ cm

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(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.
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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 $Δ D E F$ .