Question

The dimensions of a blackboard are 9/10 of a meter. In a drawing of a blackboard given below, 1/2 of an inch represents 2 meters.

Answer 1

16m² per in²

Explanation:

Here is the complete question: The dimensions of a blackboard are 9/10 of a meter by 7/10 of a meter. In a drawing of a blackboard given below, 1/2 of an inch represents 2 meters. What is unit rate of area in square meters of the blackboard per square inch of area in drawing?

Given: Dimension of blackboard=
`((9)/(10) * (7)/(10) ) of a meter`

In a drawing, 1/2 of an inch represents 2 meters.

Now, finding scale of drawing

As given; 1/2 of an inch represents 2 meters

∴
`(1)/(2)/ 2= (1)/(4)  (in)/(m)`

Fraction shows that 1 inch represent 4 meter in drawing.

Next, converting the unit of dimensions of the blackboard.

`(9)/(10)\ m= (9)/(10) / 4` =
`(9)/(40)` in

`(7)/(10)\ m= (7)/(10) / 4= (7)/(40)` in

Now, finding area of blackborad in m²

Area of blackboard=
`((9)/(10) * (7)/(10) )</p><p>∴ Area of blackboard= [tex](63)/(100) \ m^(2)`

Next, Area of blackboard in drawing

Area of blackboard in drawing=
`(9)/(40)* (7)/(40)= (63)/(1600) in^(2)`

∴ Unit rate of area in square meters of the blackboard per square inch of area in drawing:

`(63)/(100)/ (63)/(1600)`

To divide the fraction take the reciprocal of divisor and multiply the dividend.

`(63)/(100) * (1600)/(63)= (1600)/(100)`

∴ 16
`(m^(2) )/(in^(2) )` is the unit rate of area in square meters of the blackboard per square inch of area in drawing.