∆DEF and ∆GHI are two similar triangles. If DE = 64 cm, GH = 24 cm, and the perimeter of ∆GHI is 72 cm, then what is the sum of the lengths (in cm) of the sides EF and FD of the ∆DEF?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 128.
∆DEF ~ ∆GHI
So,
ED/GH = Perimeter of ∆DEF/Perimeter of ∆GHI
⇒ 64/24 = Perimeter of ∆DEF/72
Perimeter of ∆DEF = 64/24 × 72
Perimeter of ∆DEF = 64 × 3 = 192 cm
In ∆DEF
⇒ DE + DF + EF = 192
⇒ 64 + DF + EF = 192
⇒ DF + EF = 192 - 64
⇒ DF + EF = 128