Question

The actual width ( w) of a regulation soccer field is 90 meters (m), and the actual length is 120 meters (m). A coach has drawn a scale model of the field on a blackboard. If the longest side of his drawing is 18 cm, how long is the other side of the drawing( w)?

Answer 1

Proportion states that the two equal ratios or fractions are equal.

Use conversion:

1 m = 100 cm

As per the statement:

The actual width ( w) of a regulation soccer field is 90 meters (m), and the actual length is 120 meters (m

⇒Actual length = 120 m and Actual width = 90 m

It is also given that:

A coach has drawn a scale model of the field on a blackboard. If the longest side of his drawing is 18 cm.

⇒ Drawing length = 18 cm = 0.18 m

By definition of proportion:

`\frac{\text{Actual length}}{\text{Actual width}}=\frac{\text{Drawing length}}{\text{Drawing width}}`

Substitute the given values we have;

`(120)/(90)=\frac{0.18}{\text{Drawing width}}`

By cross multiply we have;

`120 \cdot \text{Drawing width} = 90 \cdot 0.18`

Simplify:

`120 \cdot \text{Drawing width} =16.2`

Divide both sides by 120 we get;

`\text{Drawing width} =0.135` m

Or

`\text{Drawing width} =13.5` cm

Therefore, the other side of the drawing width is 13.5 cm