A plot has a 3:2 length-to-breadth ratio. If breadth is 40m less than length, what is the plot's perimeter?
Show answer Hide answer
Answer: C. 400m
Explanation
Subtracting breadth from length yields a difference of exactly one variable unit equal to 40 meters. Multiplying the scaling factor by three gives a length of 120 meters for the plot. Calculating the perimeter using twice the sum of length and breadth results in exactly 400 meters. Rectangular perimeters are determined by adding together the lengths of all four outer boundary sides. Algebraic ratio problems use a common variable multiplier to represent unknown linear dimensions accurately. The perimeter formula for any standard rectangle equals two multiplied by the sum of its length and breadth.
Option A overestimates the perimeter by miscalculating the underlying linear dimensions derived from the given ratio. Option B underestimates the perimeter because it fails to account for both pairs of opposite sides correctly. Option D results from an incorrect algebraic setup that distorts the relationship between length and breadth.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A cylinder has a 2r radius and a 3r height. Find its curved surface area.
Show answer Hide answer
Answer: C. 12 πr2 sq units
The curved surface area formula requires multiplying two by pi, the radius, and the height. Substituting the given dimensions into the formula yields two multiplied by pi by two r by three r. Multiplying these numerical...
Q2. The current mean age of a married pair and their daughter is 35 years. Fifteen years ahead, the mother's age will match the combined current ages of the father and daughter. Determine the mother's current age.
Show answer Hide answer
Answer: D. 45 years
Setting up simultaneous linear equations for the family ages reflects the current mean of thirty five years. Accounting for the fifteen year future age shift matches the mother's age to the combined current ages. Solving...
Q3. What is the ratio of a square's area to the area of a square constructed on its diagonal?
Show answer Hide answer
Answer: D. 1:2
The original square has an area equal to side length squared using standard geometric principles. Constructing a square on the diagonal creates a new figure with side length multiplied by root two. Squaring the new diago...
Q4. What is the volume ratio of a cube to the sphere fitted perfectly inside it________?
Show answer Hide answer
Answer: D. 6: π
The volume of a cube with side length a is determined by cubing the side dimension value. A sphere fitted perfectly inside has a radius equal to half of the cube side length. Dividing the cube volume by the sphere volume...
Q5. What are the roots of the quadratic equation 3x2 – 12x + 10 = 0?
Show answer Hide answer
Answer: D. irrational and unequal
Calculating the discriminant for three x squared minus twelve x plus ten equals fourteen minus one twenty. The resulting discriminant value of twenty four is positive but fails to form a perfect square. Quadratic equatio...
Q6. Two numbers are in a 5:9 ratio. Reducing each by 5 changes the ratio to 5:11. Find the numbers.
Show answer Hide answer
Answer: D. 15, 27
Representing the numbers as algebraic multiples allows setting up a fractional equation for reduction. Subtracting five from both terms and equating the result to five over eleven forms the correct expression. Solving th...