Question

Plz give me answer fast

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Answer 1

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1) "When 2 ∆s are similar, the ratio of areas of those ∆s is equal to the ratio of the squares of their corresponding sides." Therefore, the ratio of areas of the ∆s :-

$\sf{ \frac{ {3}^{2} }{ {5}^{2} } = \frac{9}{25} }$

Therefore, the ratio of their areas are 9 : 25.

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2)

$\sf{tan\theta \: = \: \sqrt{3} }$

$\sf{\implies \: tan\theta \: = tan60° }$

Cut off tan on both sides,

$\sf{\theta \: = 60°}$

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3) (See attachment) It is given that ABCD is a square,

Let us assume that AB = BC = CD = DA = a

According to Pythagoras theorem,

$\sf{(AB)} ^{2} + {(AD)}^{2} = {(BD)}^{2}$

$\sf{\implies \: {a}^{2} + \: {a}^{2} = 10^{2} }$

$\sf{\implies \: 2 {a}^{2} = \: 100}$

$\sf{\implies \: {a}^{2} = \: \frac{100}{2} = 50 }$

$\sf{\therefore \: a = \sqrt{50} = 5 \sqrt{2} cm}$

Therefore, side = 5√2 cm.

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4) Radius of one circle r1 = 5.5cm

Radius of another circle r2 = 4.2cm

Since the circle touches each other externally.

Therefore,

Distance between there centers,

r1 + r2

= 5.5cm + 4.2cm

= 9.7cm.

Therefore, the distance between their centres are 9.7cm

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