Question

Find the length of RP, if P divides the line segment $ RS = 2cm $ in the ratio of $ 3:2 $
 $
  A.{\text{ 1}}{\text{.6cm}} \\
  {\text{B}}{\text{. 2}}{\text{.4cm}} \\
  {\text{C}}{\text{. 1}}{\text{.2cm}} \\
  {\text{D}}{\text{. None of these}} \\
  $

Answer 1

Hint: Here, first draw the line with the given specifications and convert the given ratio in the mathematical equation taking any reference value as “x” and then simplify the equation. Find the unknown and then place the value.

Complete step-by-step answer:
Given that the P divided the line segment $ RS = 2cm $ in the ratio of $ 3:2 $

Let the RP $ = 3x $
And PS $ = 2x $
We know that
 $ RS = RP + PS $
Place the given values in the above equation.
 $ 2 = 3x + 2x $
Simplify the above equation and make the unknown “x” as the subject-
 $ 2 = 5x $
When number in multiplicative changes its side, it goes to the division and vice versa
 $
   \Rightarrow x = \dfrac{2}{5} \\
   \Rightarrow x = 0.8 \\
  $
Now, the required length RP $ = 3x $
Place the value of “x” in the above equation
RP $ = 3(0.8) $
RP $ = 2.4cm $

So, the correct answer is “Option B”.

Note: Always convert the given word statement in the correct mathematical form and simplify using basic mathematical operations. Ratio is the comparison between two numbers without any units. Whereas, when two ratios are set equal to each other are called proportion. Four numbers a, b, c, and d are said to be in proportion. If $ a:b = c:d $ whereas, four numbers are said to be in continued proportion if $ a:b = b:c = c:d $ . Do not forget to write the given respective units in the resultant answer.