A rectangular plot's length is twice its breadth. Given an area of 6075 sq meters, what is its length?
Show answer Hide answer
Answer: C. 135m
Explanation
Setting breadth to x and length to two x creates an area equation of two x squared equals sixty seventy five. Dividing sixty seventy five by two and taking the square root gives the breadth value. Multiplying the breadth by two yields the final calculated length of one hundred thirty five meters. Area of a rectangle is determined by multiplying its width by its length dimensions. When length is a multiple of breadth the area equation simplifies to a solvable quadratic form. Extracting square roots allows recovering linear dimensions from total area measurements.
Land surveyors calculate plot dimensions from total area surveys for real estate documentation. Agricultural planning requires knowing field lengths and widths for irrigation and crop planting. Geometric proportion problems help reinforce algebraic problem-solving skills in practical contexts. Option A suggests forty five meters which yields an area far smaller than given. Option B suggests seventy five meters which does not satisfy the double length relationship. Option D is incorrect because option C accurately provides the required length value.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A rectangular plot's length increases by 25%. To keep the area unchanged, by what percent should the width be altered___________?
Show answer Hide answer
Answer: D. Reduced by 20%
Increasing the length of a rectangle by twenty five percent multiplies its length dimension by a factor of five over four. To keep the overall area completely unchanged, the width must be multiplied by the reciprocal fac...
Q2. A rectangle's length is two-fifths of a circle's radius. The circle's radius matches the side of a square with a 1225 sq unit area. What is the rectangle's area given a 10-unit breadth?
Show answer Hide answer
Answer: A. 140
The square root of twelve hundred twenty five establishes the circle radius as thirty five. Taking two fifths of thirty five gives the exact length of the target rectangle. Multiplying the calculated length of fourteen b...
Q3. The interest on Rs. 750 over 2 years equals the true discount on Rs. 960 due in 2 years. Assuming equal interest rates, find the rate:
Show answer Hide answer
Answer: B. 14%
Simple interest and true discount formulas are equated based on the problem statement conditions. Setting up the algebraic relationship for both monetary values over two years isolates the rate. Solving the resulting fin...
Q4. A rectangle's length is triple its breadth with a 96 m perimeter. Find its area.
Show answer Hide answer
Answer: A. 432 sq m
The perimeter of a rectangle is calculated by taking twice the sum of its length and breadth. Given that the length is triple the breadth, the perimeter expression simplifies to eight times the breadth equaling ninety si...
Q5. A rectangular field's length is twice its width and contains an 8m square pond. If the pond's area is 1/8th of the field, what is the field's length?
Show answer Hide answer
Answer: B. 32 m
An eight meter square pond has an area equal to sixty four square meters. Multiplying sixty four square meters by eight gives the total field area of five hundred twelve. Solving the equation where length equals twice th...
Q6. What rope length is needed to tether a cow to graze an area of 9856 sq m:________?
Show answer Hide answer
Answer: A. 56m
The area grazed by a tethered animal forms a circular region around the tether point. Dividing the total grazed area by pi and taking the square root determines the circular radius. The calculated radius equals fifty six...