3 On the scale of a map, 4 cm represent 20 km. If the distance between two points is 10 cm, what is the actual distance between these points? (Hint: Find the scale for 1 cm and multiply it by 10.)
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3 On the scale of a map, 4 cm represent 20 km. If the distance between two points is 10 cm, what is the actual distance between these points? (Hint: Find the scale for 1 cm and multiply it by 10.)
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Answer:
The points which are 10 cm apart on map, they actually have distance of 50 km between them.
Step-by-step explanation:
Given that, On the scale of a map, 4 cm represent 20 km. (i.e 20 × 1000 × 100 = 2000000 cm)
It means, scale of a map is given as 4 : 2000000 i.e 1 : 500000 and two points are 10 cm apart on the map.
We have to find, the actual distance between the points.
Now, the scale of a map and distance between two points are in direct variation.
Let assume that actual distance between the two points be x cm.
So, According to law of direct variation, we get
[tex]\qquad\sf \: \dfrac{1}{500000} = \dfrac{10}{x} \\ \\ [/tex]
[tex]\sf \: x = 10 \times 500000 \\ \\ [/tex]
[tex]\sf \: x = 5000000 \:cm \\ \\ [/tex]
[tex]\qquad\sf\implies \sf \:x = 50 \: km \: \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Hence,
The points which are 10 cm apart on map, they actually have distance of 50 km between them.
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]