Question

Triangles ABC and DEF are similar and their areas are 144cm2 and 81cm2 respectively. If EF = 8 cm, what is BC ?

Answer 1

Answer:

Second Option

Step-by-step explanation:

Given :-

∆ABC and ∆DEF are similar and their areas are 144 cm² and 81 cm² respectively.

To find :-

If EF = 8 cm then Find BC ?

Solution :-

Given that

∆ABC and ∆DEF are similar triangles

EF = 8 cm

We know that

" The ratio of the areas of the two similar triangles is equal to the ratio of the squares of the corresponding sides".

=> Ar(∆ABC)/Ar(∆DEF) = (AB/DE)²= (BC/EF)²

= (AC/DF)²

We have,

Ar(∆ABC)/Ar(∆DEF) = (BC/EF)²

=> 144/81 = (BC/8)²

=> BC/8 = √(144/81)

=> BC /8 = 12/9

On applying cross multiplication then I

=> 9×BC = 8×12

=> 9×BC = 96

=> BC = 96/9

=> BC = 32/3 cm

Answer :-

The length of BC = 32/3 cm

Used formulae:-

→ " The ratio of the areas of the two similar triangles is equal to the ratio of the squares of the corresponding sides".

Step-by-step explanation:

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