Question

A room is 16 m long and 8.5 m wide. If a square carpet of 10.5 m is laid on the floor, then find the area which is left uncarpeted.​

Answer 1

Area of room = length × breadth

                      = 16×8.5

                        = 136 m²

Area of carpet = a² {a = side of the square}

                        = 10.5×10.5

                        = 110.25m²

Area left uncarpeted = Area of room - Area of carpet

                                   = 136 - 110.25

                                  = 25.75 m²

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION } \mid}}}}}$

Given,

Length of the rectangular room = 16 m

Width of the rectangular room = 8.5 m

Length of a side of the square carpet = 10.5 m

The square carpet of 10.5 m is laid on the floor of the 16 m long and 8.5 m room.

To find :

The area which is left uncarpeted = ?

We know that,

$\boxed{ \sf{ \: 1. \: Area \: \: of \: \: a \: \: rectangle = Length \times Width \: }} \\ \\ \boxed{ \sf{ \: 2. \: Area \: \: of \: \: a \: \: square = Side \times Side}}$

Using these two formulas to find the area of the room and area of the carpet :

↬ Area of the room = Length × Width

= 16 m × 8.5 m

= 136 m²

↬ Area of the carpet = Side × Side

= 10.5 m × 10.5 m

= 110.25 m²

∴ The area which is left uncarpeted = Area of the room - Area of the carpet

= 136 m² - 110.25 m²

= 25.75 m²

So, when the square carpet of 10.5 m is laid on the floor of the room 16 m long and 8.5 m wide, then the area left uncarpeted is 25.75 m².