(d) If ABC – PQR, AB = 6.5 cm, PQ = 10.4 cm and
perimeter of ABC = 60 cm, then find the
perimeter of APQR.
Answers
Answer:
ΔABC ~ Δ PQR
=> (AB/PQ ) = (BC/QR) = (AC/PQ).
=> (AB/PQ ) = (BC/QR) = (AC/PQ) = (AB+BC+AC)/(PQ+QR +PR)
=> (AB/PQ ) = (Perimeter of ΔABC) /(perimeter of ΔPQR)
=> (6.5/10.4) = 60/(Perimeter of ΔPQR).
=> Perimeter of ΔPQR = 96 cm.
[ Note 1 : a/b = c/d. ……(1)
=> a/c = b/d. (Alterendo)
=> (a+c)/c = (b+d)/d. ( Componendo : Adding 1 to both sides)
=> (a+c)/(b+d) = c/d. (Alterendo)
Thus by (1)…
a/b = c/d = (a+c)/(b+d).
Similarly,
a/b =c/d =e/f = (a+c+e)/(b+d+f) (= Sum of antecedents / Sum of consequents)
Note 2 : In the ratio a/b ,
a = antecedent
b = consequent.]
Answer:AB/PQ=BC/QR=AC/PR
AB/PQ=6.5/10.4=5/8
AB/PQ=BC/QR=AC/PR=5/8 ......1
AB+BC+CA=PERIMETER OF TRIANGLE ABC=60 . ...
from 1
AB=5/8PQ ,BC=5/8QR ,AC=5/8PR
from2
5/8PQ + 5/8QR+ 5/8PR= 60
5/8(PQ+QR+PR)=60
perimeter of triangle PQR = 60×8/5
=12×8
= 96c.my ANSWER
perimeter of triangle PQR =96 c.m
ANS
Step-by-step explanation: