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Question
In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is ______.
Options
22.5 cm
25 cm
27 cm
30 cm
MCQ
Fill in the Blanks
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Solution
In ΔABC, it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also, ΔDEF is given such that EF = 8 cm and ΔDEF ~ ΔABC. Then, perimeter of ΔDEF is 30 cm.
Explanation:
Because ΔDEF ~ ΔABC the vertex order gives D ↔ A, E ↔ B, F ↔ C, so EF corresponds to BC and corresponding sides are in the same ratio.
Thus, scale factor `k = (EF)/(BC)`
= `8/6`
= `4/3`
Perimeter of ABC = 9 + 6 + 7.5
= 22.5 cm
Perimeter of DEF = k × 22.5
= `4/3 xx 22.5`
= 30 cm
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