Question

sides of equilateral triangle ABC,DEF are 4cm and 5cm. find ar(∆DEaf)/ar(∆ABC)​

Answer 1

Answer:

Ratio of areas of ∆ = (ratio of corresponding sides)²

(∆DEF)/(∆ABC) = 5²/4² = 25/16 (Ans)

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Answer 2

$\dfrac{ar(\triangle DEF)}{ar(\triangle ABC)}=\dfrac{25}{16}$

Step-by-step explanation:

Side of equilateral triangle, ABC = 4 cm

Side of equilateral triangle, DEF = 5 cm

As we know two equilateral triangle is similar. If two triangles are similar then ratio of their area is equal to ratio of square of their sides.

$\dfrac{ar(\triangle DEF)}{ar(\triangle ABC)}=\dfrac{DE^2}{AB^2}$

where, DE = 5 cm and AB = 4 cm

$\dfrac{ar(\triangle DEF)}{ar(\triangle ABC)}=\dfrac{5^2}{4^2}$

$\dfrac{ar(\triangle DEF)}{ar(\triangle ABC)}=\dfrac{25}{16}$

Hence, the ratio of ar(ΔDEF) and ar(ΔABC) is 25:16

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