Question

it is it is given that triangle ABC is similar to triangle d e f and the corresponding side of these Triangles are in ratio 5 ratio 9 then area of triangle ABC ratio area of triangle d e f will be ​

Answer 1

Answer:

$\frac{ar(abc)}{ar(def)} = \frac{ {ab}^{2} }{ {de}^{2} } \\ = \frac{ {5}^{2} }{ {9}^{2} } \\ = \frac{25}{81}$

Answer 2

The ratio of the area of triangle ABC and the area of triangle DEF will be ​25/81.

Step-by-step explanation:

It is given that,

∆ABC ~ ∆DEF

The ratio of the corresponding side of the similar triangles are 5:9

Now, we know that when the two given triangles are similar, then the ratio of there areas is equal to the ratio of the square of their corresponding sides.

∴ [Area of the ΔABC] / [Area of the ΔDEF] = $\frac{AB^2}{DE^2} = \frac{BC^2}{EF^2} = \frac{AC^2}{DF^2}$

Substituting the given ratio as 5/9

∴ [Area of the ΔABC] / [Area of the ΔDEF] = [5²] / [9²]

⇒ [Area of the ΔABC] / [Area of the ΔDEF] = [25] / [81]

⇒ [Area of the ΔABC] / [Area of the ΔDEF] = 25:81

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