Scales 3
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Question 1 of 3
1. Question
A map indicates that the distance between a town to the beach is `65 \text(cm)`. If the scale of the map is `1:50 000`, what is the actual distance between the town and the beach in kilometres?
- (32.5) `\text(km)`
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A scale is the ratio of the size of a model to the actual object it represents.Quad boxes are used to easily find ratesFirst, fill up the quad boxes with the three known values and have the unknown value be `x`.Map Land `1` `50 000` `65` `x` Next, equate the two columns and solve for `x`.`1/(65)` `=` `(50 000)/x` `1(x)` `=` `50 000(65)` Cross multiply `x` `=` `3 250 000` Since the given measurement for the map is in `\text(cm)`, this value will be `3 250 000 \text(cm)`.Finally, convert the centimetres into kilometres.`1 \text(kilometre)` `=` `100 000 \text(centimetres)` `x` `=` `3 250 000xx1/(100 000)` `100 000cm` has `5` zeroes `:.` move `5` decimal places to left `x` `=` `(3 250 000)/(100 000)` `=` `32.5` `x=32.5 \text(km)` -
Question 2 of 3
2. Question
A model plane has a wingspan of `61 \text(cm)`. What would the actual wingspan be in metres if the scale is `1:22`?
- (13.42) `\text(m)`
Hint
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A scale is the ratio of the size of a model to the actual object it represents.Quad boxes are used to easily find ratesFirst, fill up the quad boxes with the three known values and have the unknown value be `x`.Model Actual `1` `22` `61` `x` Next, equate the two columns and solve for `x`.`1/(22)` `=` `(61)/x` `1(x)` `=` `61(22)` Cross multiply `x` `=` `1342` Since the given measurement for the model is in `\text(cm)`, this value will be `1342 \text(cm)`.Finally, convert the centimetres into metres.`1 \text(metre)` `=` `100 \text(centimetres)` `x` `=` `1342xx1/(100)` `100cm` has `2` zeroes `:.` move `2` decimal places to left `x` `=` `(1342)/(100)` `=` `13.42` `x=13.42 \text(m)` -
Question 3 of 3
3. Question
A building plan indicates that the building’s length will be `70 \text(cm)`. If the scale is `1:50`, what would the actual length of the building be in metres?
- (35) `\text(m)`
Hint
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Incorrect
A scale is the ratio of the size of a model to the actual object it represents.Quad boxes are used to easily find ratesFirst, fill up the quad boxes with the three known values and have the unknown value be `x`.Model Actual `1` `50` `70` `x` Next, equate the two columns and solve for `x`.`1/(70)` `=` `(50)/x` `1(x)` `=` `50(70)` Cross multiply `x` `=` `3500` Since the given measurement for the plan is in `\text(cm)`, this value will be `3500 \text(cm)`.Finally, convert the centimetres into metres.`1 \text(metre)` `=` `100 \text(centimetres)` `x` `=` `3500 000xx1/(100)` `100cm` has `2` zeroes `:.` move `2` decimal places to left `x` `=` `(3500)/(100)` `=` `35` `x=35 \text(m)`