State whether the statement is true or false. If the plan and measurement for a house are given, and the house is surrounded by a path 1m wide, then the cost of paving the path with bricks at a rate of Rs. 120 per

m
2

will be Rs. 4000.

Question

State whether the statement is true or false.

If the plan and measurement for a house are given, and the house is surrounded by a path 1m wide, then the cost of paving the path with bricks at a rate of Rs. 120 per $m 2$ will be Rs. 4000.

m
    2

will be Rs. 4000.

Accepted Answer

We have been given,Cost of paving the path = Rs. 120 per m2.We know, the area of a rectangle is the product of its length and its breadth.Thus, the cost of paving the path with bricks will be,Area of triangle ABCD – Area of triangle PQRS.Let’s calculate the area of triangle ABCD.Area of the rectangle ABCD = length × breadthLength of AB = PQ + 1m path= 1 + 4 + 2.5 + 4 + 1= 10.5 + 2=12.5Breadth of BC = PS + 1m path= 1 + 3 + 3 + 1= 6 + 2= 8Substituting the values,= 12.5 × 8

m
    2

=100

m
    2

Similarly, calculating the area of triangle PQRS.Area of the rectangle PQRS = length × breadthLength = PQ= 4 + 2.5 + 4= 10.5Breadth = PS= 3 + 3= 6 Substituting the values,10.5×6= 63