Question

In ∆ XYZ, XY = 8 cm, YZ = 12 cm, XZ = 10 cm, If ∆ XYZ ~ ∆ PQR and
PQ = 4 cm then find the lengths of remaining sides of ∆ PQR.
pl answer step by step

Answer 1

Answer:

QR=24 cm

PR=20cm

Step-by-step explanation:

Because Triangle ABC AND TRIANGLE PQR ARE CONGRUENT TO EACH OTHER AND

IN RATIO OF 2:1

SO QR=2×YZ

=2×12

= 24 cm

Answer 2

Solution :-

given that, In ∆XYZ ,

→ XY = 8 cm

→ YZ = 12 cm

→ XZ = 10 cm

and, In ∆PQR ,

→ PQ = 4 cm .

also,

→ ∆XYZ = ∆PQR

So,

→ XY/PQ = YZ/QR = XZ/PR { when two ∆'s are similar , their corresponding sides are in same ratio . }

then, putting values we get,

→ XY/PQ = 8/4 = 2/1

therefore,

→ YZ/QR = 2/1

→ 12/QR = 2/1

→ 2QR = 12

→ QR = 6 cm

and,

→ XZ/PR = 2/1

→ 10/PR = 2/1

→ 2PR = 10

→ PR = 5 cm

hence, the lengths of remaining sides of ∆PQR are 6 cm and 5 cm .

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