Question

Amit started cycling along the boundaries of a square field from cover point $A$. After half an hour, he reached the comer point $C$, diagonally opposite to $A$. If his speed was $8 \mathrm{~km} / \mathrm{hr}$, what is the area of the field in square $\mathrm{km}$ (a) 64 (b) 8 (c) 4 (d) Cannot be determined

Name: Problem 52, Chapter 15: The Pearson Guide to Objective Arithmetic for Competitive Examinations
Uploaded: 2021-10-10T14:25:08-08:00
Duration: 2 min 52 s
Channel: Dheeraj Sharma
Description: Amit started cycling along the boundaries of a square field from cover point A. After half an hour, he reached the comer point C, diagonally opposite to A. If his speed was 8 km / hr, what is the area of the field in square km (a) 64 (b) 8 (c) 4 (d) Cannot be determined

    Amit started cycling along the boundaries of a square field from cover point $A$. After half an hour, he reached the comer point $C$, diagonally opposite to $A$. If his speed was $8 \mathrm{~km} / \mathrm{hr}$, what is the area of the field in square $\mathrm{km}$
(a) 64
(b) 8
(c) 4
(d) Cannot be determined

The Pearson Guide to Objective Arithmetic for Competitive Examinations

Dinesh Khattar 2nd Edition

Chapter 15, Problem 52

Instant Answer

Solved by Expert Dheeraj Sharma

10/10/2021

Step 1

Since his speed is $8 \mathrm{~km/hr}$, we can calculate the distance he covered in half an hour (which is $0.5$ hours) using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Substituting the values: \[ \text{Distance} = 8 Show more…

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Amit started cycling along the boundaries of a square field from cover point $A$. After half an hour, he reached the comer point $C$, diagonally opposite to $A$. If his speed was $8 \mathrm{~km} / \mathrm{hr}$, what is the area of the field in square $\mathrm{km}$ (a) 64 (b) 8 (c) 4 (d) Cannot be determined

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Key Concepts

Properties of a Square

A square is a regular quadrilateral with equal side lengths and right angles. Its properties, including the relationship between the side length and the perimeter, as well as the formula for computing the area, are key to solving problems involving square geometry and boundary traversal.

Uniform Motion

This concept relates the distance traveled to the speed and time of travel. It is based on the fundamental formula: distance = speed × time, which is widely used in problems involving constant speed movement.

Perimeter Traversal in Polygons

When an object moves along the boundary of a polygon, the total distance traveled can be expressed as the sum of one or more side lengths. Recognizing portions of the perimeter and relating them to the dimensions of the polygon is essential in many geometric problems.

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