Question

The distance between a school and the house of a girl is given by 5 cm in the picture, using the scale 1 cm : 5 km. Find the actual distance between the two places.

Answer 1

Hint:
Here, we need to find the actual distance between the school and the house. We will find the actual distance by using the given scale and multiplying it such that the 1 cm in the scale becomes 5 cm.

Complete step by step solution:
We will use the given scale to find the actual distance between the two places. The scale of the picture is given as 1 cm : 5 km. Therefore, if the distance between two places in the picture is 1 cm, the actual distance between the two places is 5 km.
We can write this as
1 cm distance in picture \[ = \] 5 km actual distance
We need to find the actual distance between the home and the school if the distance between them in the picture is 5 cm.
Multiplying both sides by 5, we get
\[1 \times 5\] cm distance in picture \[ = \] \[5 \times 5\] km actual distance
Simplifying the equation, we get
5 cm distance in picture \[ = \] 25 km actual distance

Thus, if the distance between the school and the house of the girl is given by 5 cm in the picture, then the actual distance between them is 25 km.

Note:
We can also use direct proportion to solve this problem.
Let the actual distance between the two places be \[x\] km.
If distance in picture increases, the actual distance also increases, but the scale remains the same. Therefore, we can use direct proportion to solve the problem.
Thus, using the scale and given information, we can write equate the ratios as
\[ \Rightarrow \dfrac{{1{\rm{ cm}}}}{{5{\rm{ km}}}} = \dfrac{{5{\rm{ cm}}}}{{x{\rm{ km}}}}\]
We will simplify this to find the actual distance.
Cross multiplying the terms in the expression, we get
\[ \Rightarrow 1 \times x = 5 \times 5\]
Multiplying the terms, we get
\[ \Rightarrow x = 25{\rm{ km}}\]
Therefore, the actual distance between them is 25 km.