Question

The plan of an area has shrink side that line originally \(20\) cm now measures \(19.5\) cm. If the original scale of plan is \(1\) cm \(= 10\) m, determine (i) correct distance to a measured distance of \(198\) m (ii) correct area corresponding to measured area of \(20000\ \text{m}^2\) Choose the correct answer from the options given below:

• A. (i) \(208.24\) m and (ii) \(22512.5\ \text{m}^2\)
• B. (i) \(195.88\) m and (ii) \(18743.76\ \text{m}^2\)
• C. (i) \(204.12\) m and (ii) \(21256.24\ \text{m}^2\)
• D. (i) \(212.36\) m and (ii) \(17486.76\ \text{m}^2\)

Hint:

For shrunk maps or plans: Linear correction: \[ \boxed{ \frac{\text{Original length}} {\text{Shrunk length}} } \] Area correction: \[ \boxed{ \left( \frac{\text{Original length}} {\text{Shrunk length}} \right)^2 } \] Remember: \[ \boxed{ \text{Area corrections always use square of linear correction} } \]

Answer 1

The Correct Option is A