Question
Download Solution PDFIf ΔABC and ΔPQR are similar. AB = 8 cm, PQ = 12 cm, QR = 18 cm and RP = 24 cm, then the perimeter of ΔABC is _________ cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :-
ΔABC and ΔPQR are similar
AB = 8 cm
PQ = 12 cm
QR = 18 cm
RP = 24 cm
Concept Use :-
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
(1) AB/PQ = BC/QR = AC/PR
(2) angle A = angle P , angle B = angle Q , angle C = angle R
Calculation :-
⇒ AB/PQ = BC/QR = AC/PR
⇒ 8/12 = BC/18 = AC/24
⇒ BC = (18 × 8) /12 = 12cm
and,
⇒ AC = (12 × 24) /18 = 16 cm
Now,
⇒ Perimeter of triangle ABC = AB +BC + AC = 8 + 12 + 16
⇒ Perimeter of triangle ABC = 36cm
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