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.

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= [tex](\frac{9}{10} \times \frac{7}{10} ) of a meter[/tex]

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

∴ [tex]\frac{1}{2}\div 2= \frac{1}{4} \frac{in}{m}[/tex]

Fraction shows that 1 inch represent 4 meter in drawing.

Next, converting the unit of dimensions of the blackboard.

[tex]\frac{9}{10}\ m= \frac{9}{10} \div 4[/tex] = [tex]\frac{9}{40}[/tex] in

[tex]\frac{7}{10}\ m= \frac{7}{10} \div 4= \frac{7}{40}[/tex] in

Now, finding area of blackborad in m²

Area of blackboard= [tex](\frac{9}{10} \times \frac{7}{10} )

∴ Area of blackboard= [tex]\frac{63}{100} \ m^{2}[/tex]

Next, Area of blackboard in drawing

Area of blackboard in drawing= [tex]\frac{9}{40}\times \frac{7}{40}= \frac{63}{1600} in^{2}[/tex]

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

[tex]\frac{63}{100}\div \frac{63}{1600}[/tex]

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

[tex]\frac{63}{100} \times \frac{1600}{63}= \frac{1600}{100}[/tex]

∴ 16 [tex]\frac{m^{2} }{in^{2} }[/tex] is the unit rate of area in square meters of the blackboard per square inch of area in drawing.