A rectangle's length is halved while its breadth is tripled. What is the percentage change in area?
Show answer Hide answer
Answer: B. 50% increase
Explanation
The original area of the rectangle is calculated by multiplying its length and breadth together. Halving the length and tripling the breadth creates a new area equal to one point five times the original. Comparing the new area to the original reveals a net increase of fifty percent overall. Area represents the two dimensional space enclosed within the boundaries of a geometric flat figure. Percentage change measures the relative difference between an initial value and a final modified value. Multiplication factors scale dimensions directly, compounding their proportional effects upon the final calculated area.
Businesses apply scaling factors regularly when adjusting product dimensions while attempting to optimize material costs. Understanding dimensional scaling helps engineers predict how structural changes will impact total surface coverage requirements. Mastering area calculations is essential for fields like architecture, interior design, and urban land development. A twenty five percent increase would incorrectly assume a much smaller scaling factor combination. A fifty percent decrease completely reverses the mathematical direction of the actual calculated area change. A seventy-five percent decrease ignores the tripling effect applied to the breadth dimension of the shape.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Two numbers in a 1:4 ratio have an H.C.F of 84 and an L.C.M of 21. What is the larger number____________?
Show answer Hide answer
Answer: C. 84
Two numbers sharing a given ratio can be expressed with variables representing their proportional parts. The product of two numbers always equals the product of their highest common factor and least common multiple. Appl...
Q2. Three metal cubes with edges of 3 dm, 4 dm, and 5 dm are melted into a single cube. Find the new edge.
Show answer Hide answer
Answer: D. 6 dm
The volume of each metal cube is found by cubing its respective decimeter edge length. Adding the individual volumes together gives a cumulative total volume of two hundred sixteen cubic decimeters. Taking the cube root...
Q3. A playground measures 36 m by 21 m. How many flagstaffs are needed along the boundary placed 3 m apart___________?
Show answer Hide answer
Answer: B. 38
The perimeter of any closed rectangular boundary is calculated by adding length and breadth then doubling. Dividing this total calculated perimeter by the specific flagstaff spacing distance determines the total count. P...
Q4. What is the smallest square number divisible by 8, 12, and 18________?
Show answer Hide answer
Answer: D. 144
Finding the least common multiple of eight, twelve, and eighteen yields a base value of seventy-two. Prime factorization of seventy-two reveals factors that lack complete squared pairings for all primes. Multiplying seve...
Q5. A rectangle's length and breadth are in a 5:4 ratio. Find its perimeter if its area is 180 cm²
Show answer Hide answer
Answer: A. 54 cm
Algebraic variables represent the length and breadth using the given five to four ratio. Multiplying length and breadth gives an area expression that equals one hundred eighty square centimeters. Solving for the variable...
Q6. A rectangle's length increases by 60%. By what percentage must its width be reduced to keep the area unchanged?
Show answer Hide answer
Answer: A. 37 ½ %
Preserving total rectangle area requires multiplying the adjusted width by the reciprocal of the length factor. An increase in length by sixty percent scales the initial linear dimension by a factor of one point six. Mul...