A rectangle has an area of 12 sq meters and a length 3 times its breadth. What is its perimeter?
Show answer Hide answer
Answer: D. None of these
Explanation
The calculated breadth of two meters and length of six meters satisfy the given area equation. Evaluating the perimeter formula with these dimensions yields sixteen meters as the final result. Since sixteen meters is missing from the listed choices, none of these options is correct. Rectangle area is determined by multiplying its length by its breadth. The perimeter of a rectangle equals twice the sum of its length and breadth. Algebraic substitution allows solving unknown side lengths when area relationships are clearly defined.
Finding rectangle dimensions is common in construction when planning room layouts and flooring materials. Property boundaries and fencing projects require accurate perimeter and area calculations for budgeting. Basic algebraic modeling bridges the gap between geometric properties and numerical problem solving. Option a suggests a perimeter of fourteen meters which contradicts the correct calculated dimension sum. Option b proposes an eighteen meter perimeter that does not match the derived rectangle side lengths. Option c provides an extremely small value that represents neither the perimeter nor the side dimensions.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A rectangle's area is three times that of a square. Its length is 40 cm, and its breadth is (3/2) times the square's side. Find the square's side in cm__________?
Show answer Hide answer
Answer: B. 20
The rectangle area formula uses length multiplied by breadth expressed in terms of square side x. Equating rectangle area to three times square area creates a solvable algebraic equation. Dividing sixty x by three x yiel...
Q2. A parallelogram has an area of 128 sq m and an altitude twice its corresponding base. Find the base length_________?
Show answer Hide answer
Answer: A. 8 m
The geometric area of a parallelogram is calculated by multiplying its base length by its corresponding altitude. Substituting the given condition where the altitude equals twice the base gives two times the base squared...
Q3. A room's floor area is 20 m2, with the longer and shorter walls measuring 15 m2 and 12 m2 respectively. Determine the edge of the equivalent cube.
Show answer Hide answer
Answer: C. 60 m3
The square of a rectangular room volume equals the product of its three mutually perpendicular wall areas. Multiplying the floor area and two wall areas together gives thirty six hundred square units. Taking the square r...
Q4. Calculate the triangle's area given side lengths a = 1m, b = 2m, and c = 3m.
Show answer Hide answer
Answer: A. 0 sq m
The triangle inequality theorem requires the sum of any two sides exceeding the third. Adding side length one to side length two results in a sum equal to three. Because one plus two equals three the geometric condition...
Q5. A rhombus has an area of 2016 sq cm and a side of 65 cm. What are the lengths of its diagonals________?
Show answer Hide answer
Answer: B. 126cm,32cm
The geometric relationship linking a rhombus's side length and diagonals is given by side squared equaling the sum of half-diagonal squares. Testing the diagonal pair of one hundred twenty-six and thirty-two yields an ar...
Q6. A circle's area expands by 22 sq cm when its radius increases by 1 cm. What was the original radius_________?
Show answer Hide answer
Answer: C. 3 cm
The area of a circle is calculated by multiplying pi by the square of its radius. Expanding the radius by one unit creates a new area expression containing a linear term in r. Equating the area increase to twenty two all...