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

Answer:

16m² per in²

Step-by-step 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= $(\frac{9}{10} \times \frac{7}{10} ) of a meter$

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

∴ $\frac{1}{2}\div 2= \frac{1}{4} \frac{in}{m}$

Fraction shows that 1 inch represent 4 meter in drawing.

Next, converting the unit of dimensions of the blackboard.

$\frac{9}{10}\ m= \frac{9}{10} \div 4$ = $\frac{9}{40}$ in

$\frac{7}{10}\ m= \frac{7}{10} \div 4= \frac{7}{40}$ in

Now, finding area of blackborad in m²

Area of blackboard=  $(\frac{9}{10} \times \frac{7}{10} )∴ Area of blackboard= [tex]\frac{63}{100} \ m^{2}$

Next, Area of blackboard in drawing

Area of blackboard in drawing= $\frac{9}{40}\times \frac{7}{40}= \frac{63}{1600} in^{2}$

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

$\frac{63}{100}\div \frac{63}{1600}$

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

$\frac{63}{100} \times \frac{1600}{63}= \frac{1600}{100}$

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