Question

A model of the park was built on a scale of $1.5cm$to $50m$of the distance between two trees in the park is $150m$. What is the length of the model?

Answer 1

Hint: Assume the length of the model. In this we have given a scale of $1.5cm$to $50m$. It means the question is solved by writing the numbers in the ratio and then evaluating the length of the model.

Complete step by step answer:
We are given that a model of the park was built on a scale of $1.5cm$ to $50m$of the distance between two trees in the park is $150m$.
We have to find the length of the model.
Assume the length of the model corresponds to $150m$.
If we think about the given part on the question which has a scale some number to some number it means there is some ratio which has to be written to solve the question.
Write the ratio according to our question.
$\dfrac{{1.5}}{{50}} = \dfrac{x}{{150}}$
Here, we have to evaluate the value of $x$.
For this, we cross multiply the equation and solve for $x$.
$
  1.5 \times 150 = 50x \\
  50x = 225 \\
 $
Divide both the sides by $50$.
$
  \dfrac{{50x}}{{50}} = \dfrac{{225}}{{50}} \\
  x = 4.5 \\
 $
Therefore, the length of model corresponds to $150m$will be $4.5cm$.

Note: We can solve this question by another method which is given below:
We apply the concept of meter per centi-meter.
First, we are given that $1.5cm$to $50m$
If we evaluate meter per centi-meter$1.5cm$to $50m$it will be $\dfrac{{50}}{{1.5}} \approx 33.3$
Therefore, the value of meter per centi-meter is also same for $150m$ that is $33.3$
Evaluate the value of centi-meter for $150m$
$
  \dfrac{{150}}{x} \approx 33.3 \\
  x \approx 4.5 \\
 $
Hence, the length of the model corresponding to $150m$ will be $4.5cm$.