Question

In Δ XYZ, XY = 4 cm, YZ = 6 cm, XZ = 5 cm, If ΔXYZ ~ Δ​PQR and PQ = 8 cm then find the lengths of remaining sides of ΔPQR.

Answer 1

Consider, ΔXYZ ~ ΔPQR

${\displaystyle \therefore \frac{\text{XY}}{\text{PQ}}=\frac{\text{YZ}}{\text{QR}}=\frac{\text{XZ}}{\text{PR}}}$     ...[Corresponding sides of similar triangles]

⇒ ${\displaystyle \frac{4}{8}=\frac{6}{\text{QR}}=\frac{5}{\text{PR}}}$

⇒ ${\displaystyle \frac{4}{8}=\frac{6}{\text{QR}}}$  

⇒ ${\displaystyle \text{QR}=\frac{8\times 6}{4}}$

⇒ QR = 12 cm

⇒ ${\displaystyle \frac{4}{8}=\frac{5}{\text{PR}}}$

⇒ PR = ${\displaystyle \frac{8\times 5}{4}}$

⇒ PR = 10 cm

Hence, the lengths of remaining sides of ΔPQR are 12 and 10 cm.