Question

ii) AABC - ALMN, AB:LM = 8:6. Area of the larger
triangle is 48 sq.cm, then the area of the smaller
triangle is​

Answer 1

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.

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

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

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

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

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

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

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

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

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