if mn||qr,pm=6cm,qm =8cm and qr =28cm,then mn is equal to
Answers
Answer: then mn will equal to 9cm
as there pqm is a triangle and pmn is similar triangle by AA property so by using similarity we will get side of mn
let mn be x
(pm+qm)/pm=qr/mn
(6+8)/6=28/x (using cross multiplication)
x=(28*6)/14
X=9
Step-by-step explanation:
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Given :- MN || QR , PM = 6 cm, QM = 8 cm and QR = 28 cm .
To Find :- MN = ?
Solution :-
In ∆PMN and ∆PQR we have,
→ ∠PMN = ∠PQR { since MN || QR, corresponding angles }
→ ∠PNM = ∠PRQ { since MN || QR, corresponding angles }
So,
→ ∆PMN ~ ∆PQR { By AA similarity. }
then,
→ PM/PQ = MN/QR { when two ∆'s are similar their corresponding sides are in same ratio. }
→ PM/(PM + QM) = MN/QR
→ 6/(6 + 8) = MN/28
→ 6/14 = MN/28
→ 3/7 = MN/28
→ 7•MN = 28 × 3
→ MN = 4 × 3
→ MN = 12 cm (Ans.)
Hence, length of MN is equal to 12 cm .
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