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Question
If ΔАBC ~ ΔPQR, PQ = 5 cm, perimeter of ΔPQR = 20 cm, AB = 7.5 cm, then perimeter of ABC is ______.
Options
25 cm
30 cm
24 cm
32 cm
MCQ
Fill in the Blanks
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Solution
If ΔАBC ~ ΔPQR, PQ = 5 cm, perimeter of ΔPQR = 20 cm, AB = 7.5 cm, then perimeter of ABC is 30 cm.
Explanation:
Since △ABC∼△PQR, the ratio of corresponding sides equals the ratio of their perimeters.
`"Perimeter of ABC"/"Perimeter of PQR" = (AB)/(PQ)`
Substitute the given values:
`"Perimeter of ABC"/20 = 7.5/5`
`"Perimeter of ABC"/20 = 3/2`
`"Perimeter of ABC" = 20 xx 3/2`
∴ Perimeter of ABC = 30 cm
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