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Solution


Q.

Assertion (A): A vertical stick which is 15 cm long casts a 12 cm long shadow on the ground. At the same time, a vertical tower casts a 50 m long shadow on the ground, then the height of the tower is 50 m.

Reason (R): The ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
1 Both A and R are true, and R is the correct explanation of A.  
2 Both A and R are true, but R is not the correct explanation of A.  
3 A is true, but R is false.  
4 A is false, but R is true  

Ans.

(4)

Let h be the height of the tower.

Since both the tower and stick are vertical:

∠ABC=∠PQR=90°

and the angles of depression at the same instant are equal:

∠BAC=∠LQPR∴∆ABC~∆PQR(By AA similarity)ABPQ=BCQR⇒h15 cm=50 m12 cmh50=0.150.12=1512h=50×1512=1252=62.5 mThus, the height of the tower is 62.5 m, not 50 m.