Question

∆ABC ∼ ∆DEF,

If AB = 2.4 cm, DE = 1.6 cm, find the ratio of the area of ∆ABC and ∆DEF.​

Answer 1

Answer:

if both the triangles are similar,

then,

the ratio of area of triangles ABCandDEF=square of ratio of any of the corresponding sides

=(AB/DE)^2

=1.2x1.2/1.4x1.4

=36/49

= 36 : 49 ans.

Answer 2

Given-AB = 2.4 cm, DE = 1.6 cm

Find the ratio of the area of $\triangle ABC$ and ∆DFE.

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.

For similar triangles,

ratio of area of triangles = ratio of square of corresponding sides

Hence,  $\frac{Ar.\triangle ABC}{Ar.\triangle DFE} =\frac{AB^2}{DE^2}$

$\frac{Ar.\triangle ABC}{Ar.\triangle DFE} =\frac{AB^2}{DE^2}$

$\frac{Ar.\triangle ABC}{Ar.\triangle DFE} =\frac{2.4\times 2.4}{1.6\times 1.6}$

$\frac{Ar.\triangle ABC}{Ar.\triangle DFE} =\frac{9}{4}$

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