Question

.If ∆ ABC~∆MNP,BC:NP=3:4 then A(∆ABC):A(∆MNP)=_____.


9:16

3:16

27:64

3:4

​

Answer 1

Answer:

A(∆ABC):A(∆MNP) = AB^2:NP^2....(theorem of areas of similar triangles)

=3^2:4^2

=9:16

hence, A(∆ABC):A(∆MNP)=9:16

Answer 2

A(∆ABC):A(∆MNP) = 9:16

If ∆ ABC~∆MNP, then the corresponding sides are proportional. Therefore,

the ratio of the areas of the two triangles is equal to the square of the ratio of the corresponding sides.

A(∆ABC):A(∆MNP) = (BC/NP)²

=$(3/4)^2$

= $9/16$

So, the correct answer is:

A(∆ABC):A(∆MNP) = 9:16

• The formula for the area of a triangle is given by A = (1/2)bh, where b is the base and h is the height. If two triangles are similar, then the corresponding sides are proportional.
• Hence, the ratio of the areas of the two triangles is equal to the square of the ratio of the corresponding sides.

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