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प्रश्न
If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ABC.
उत्तर
According to the question,
AB = 4 cm,
DE = 6 cm
EF = 9 cm
FD = 12 cm
Also,
∆ABC ∼ ∆DEF
We have,
∴ `("AB")/("ED") = ("BC")/("EF") = ("AC")/("DF")`
⇒ `4/6 = ("BC")/9 = ("AC")/12`
By taking first two terms, we have
⇒ `4/6 = ("BC")/9`
⇒ BC = `((4 xx 9))/6` = 6 cm
And by taking last two terms, we have,
`("BC")/9 = ("AC")/12`
`6/9 = ("AC")/12`
AC = `(6 xx 12)/9` = 8 cm
Now,
Perimeter of ∆ABC
= AB + BC + AC
= 4 + 6 + 8
= 18 cm
Thus, the perimeter of the triangle is 18 cm.
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