Question

ΔABC ~ ΔPQR, A(ΔABC) = 80, A(ΔPQR) = 125 तो निम्नलिखित रिक्त चौखटों को पूरा कीजिए।

${\displaystyle \frac{\text{A}(\Delta \text{ABC})}{\text{A}(\Delta \square )}=\frac{80}{125}=\frac{\square }{\square }}$

∴ ${\displaystyle \frac{\text{AB}}{\text{PQ}}=\frac{\square }{\square }}$

Answer 1

${\displaystyle \frac{\text{A}(\Delta \text{ABC})}{\text{A}(\Delta \underline{\text{PQR}})}=\frac{80}{125}=\underline{\frac{16}{25}}}$

∴ ${\displaystyle \frac{\text{AB}}{\text{PQ}}=\underline{\frac{4}{5}}}$

[ΔABC ~ ΔPQR

∴ ${\displaystyle \frac{\text{A}(\Delta \text{ABC})}{\text{A}(\Delta \text{PQR})}=\frac{{\text{AB}}^2}{{\text{PQ}}^2}}$ ..........(समरूप त्रिभुजों के क्षेत्रफल का प्रमेय)

= ${\displaystyle \frac{80}{125}=\frac{{\text{AB}}^2}{{\text{PQ}}^2}}$

∴ ${\displaystyle \frac{{\text{AB}}^2}{{\text{PQ}}^2}=\frac{80}{125}=\frac{16}{25}}$

∴ ${\displaystyle \frac{\text{AB}}{\text{PQ}}=\frac{4}{5}}$]