Question

10- If ABC~PQR, AB=6.5cm, PQ=10.4cm and perimeter of ABC=60 cm, then
find the perimeter of PQR.​

Answer 1

Step-by-step explanation:

⭐Question:-

If ABC~PQR, AB=6.5cm, PQ=10.4cm and

perimeter of ABC=60 cm, then

perimeter of ABC=60 cm, thenfind the perimeter of PQR.

⭐Answer:-

Solution:-

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.