Question

the rectangle of a 16cm more than its breadth is same in areas as the square of side 15cm find the side of rectangle

Answer 1

Find Area:

Area of the square = 15 x 15 = 225 cm²

Formula for Area:

Area of rectangle = Length x Breadth

Define Length and Breadth:

Let the breadth be x

The length = x + 16

Solve x:

x (x + 16) = 225

x² + 16x - 225 = 0

(x - 9 )(x + 25) = 0

x = 9 or x = -25 (rejected, length cannot be negative)

Find Length and Breadth:

Breadth = x = 9 cm

Length = x + 16 = 9 + 16 = 25 cm

Answer: The sides of the rectangle are 9cm and 25cm

Answer 2

Heya !!




Let breadth of rectangle be X cm.




Length = ( X + 16 ) cm.






Area of rectangle = L × B





=> ( X + 16 ) × X





=> (X² + 16X) cm²




Side of square = 15 cm




Area of square = (15)² = 225 cm²






According to the question,





Area of rectangle = Area of square





X² + 16X = 225




X² + 16X - 225 = 0




X² + 25X - 9X - 225 = 0




X ( X + 25 ) - 9 ( X + 25 ) = 0




( X + 25 ) ( X - 9 ) = 0





( X -9 ) = 0 OR ( X + 25 ) = 0




X = 9 OR X = -25



Since , side can't be in negative . So X = 9 cm.





Breadth of rectangle = X = 9 cm



And,



Length of rectangle = X + 16 = 25 cm