Question

If the areas of two similar triangles ABC and PQR are in the ratio 9 : 16 and BC = 4.5 cm, what is the length of QR?

Answer 1

Answer:

The length of QR is 22 cm.

Step-by-step explanation:

Given:

ΔABC ~ ΔPQR.

ar(ΔABC) : ar(ΔPQR) = 9 : 16 , BC = 4.5 cm

 

ar(ΔABC)/ar( ΔPQR) = (BC/QR)²

[The ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.]

9/16 = (4.5/QR)²

(4.5/QR) = √9/16

(4.5/QR) = ¾  

3 QR = 4.5 × 4

3 QR = 18

QR = 18/3  

QR = 6 cm

Hence, the length of QR is 22 cm.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Answer

ar(ABC)/ar(PQR)=(BC)×(BC)/(QR×QR)9/16=4.5×4.5/QR×QRQR×QR=4.5×4.5×16÷9QR=√4.5×4.5×16÷9

ar(ABC)/ar(PQR)=(BC)×(BC)/(QR×QR)

ar(ABC)/ar(PQR)=(BC)×(BC)/(QR×QR)9/16=4.5×4.5/QR×QRQR×QR=4.5×4.5×16÷9QR=√4.5×4.5×16÷9QR=4.5×4/3QR=18.0÷3 QR=6cm

Answer=6cm