Chapter 3, Problem 19CR

To determine

To calculate: The length of the longer segment.

Answer to Problem 19CR

The length of the longer segment is $35$

Explanation of Solution

Given information: The lengths of two segments are in the ratio of $5:3$ and the longer segment exceeds the shorter by $14$ m is provided in the question which will help to find the solution.

Calculation: Let x be shorter segment

Then, the longer segment will be $\left(x+14\right)$

Now, according to question

  →$\frac{Longersegment}{Shortersegment}=\frac{5}{3}$

  →$\frac{\left(x+14\right)}{x}=\frac{5}{3}$

  →$3\times \left(x+14\right)=5x$

  →$3x+42=5x$

  →$42=2x$

  →$x=21$

So, the shorter segment is $21$

Now, the longer segment will be $\left(x+14\right)$

  →$21+14=35$

Conclusion: Hence, the length of the longer segment is $35$