Question

∆ABC~∆LMN ,AB:LM=8 :6 ,area of the largest traingle is 48cm²then find the area of smaller traingle
step by step explaination
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Answer 1

Answer:

Given:

Δ ABC ~ ΔLMN

AB:LM = 8:6

Area of the larger the triangle is 48 sq.cm

To find:

The area of the smaller triangle?

Solution:

We have,

AB : LM = 8 : 6

⇒ AB > LM

⇒ ΔABC > Δ LMN

⇒ Δ ABC is the larger triangle and Δ LMN is the smaller triangle

We know that,

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

∴ \frac{Area(\triangle ABC)}{Area(\triangle LMN)} = \bigg(\frac{AB}{LM}\bigg )^2

Area(△LMN)

Area(△ABC)

=(

LM

AB

)

2

substituting the given values of AB:LM = 8:6 & Area of Δ ABC = 48 cm², we get

\implies \frac{48\:cm^2}{Area(\triangle LMN)} = \bigg(\frac{8}{6}\bigg )^2⟹

Area(△LMN)

48cm

2

=(

6

8

)

2

\implies \frac{48\:cm^2}{Area(\triangle LMN)} = \frac{64}{36}⟹

Area(△LMN)

48cm

2

=

36

64

\implies Area(\triangle LMN)=\frac{48\times 36}{64}⟹Area(△LMN)=

64

48×36

\implies Area(\triangle LMN)=\frac{1728}{64}⟹Area(△LMN)=

64

1728

\implies \bold{Area(\triangle LMN)=27\:cm^2}⟹Area(△LMN)=27cm

2

Thus, the area of the smaller triangle Δ LMN is → 27 cm².

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