(0) AABC - APQR, AB : PQ = 8 : 6. If the
area of bigger triangle is 48 sq. cm then
find the area of smaller triangle.
(1) 15 sq. cm.
(2) 22 sq. cm
(3) 27 sq. cm
(4) 16 sq. cm
cm
Answers
Step-by-step explanation:
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.