The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that it’s square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is___________?
Show answer Hide answer
Answer: C. 50m
Explanation
Equal perimeters for a rectangle and square restrict their possible dimensions based on mathematical optimization principles. The square maximizes area for a given perimeter, meaning any rectangle with the same perimeter will have a smaller area. Solving the algebraic equations relating the perimeter and area differences reveals a rectangle length of fifty meters. The perimeter of a geometric shape measures the total continuous distance around its outer boundary edges. Geometric optimization proves that a square encloses the maximum possible area among all rectangles of equal perimeter. Algebraic substitution allows students to solve multi-variable systems involving geometric lengths and enclosed surface areas.
Option A proposes a length of thirty meters, which contradicts the derived algebraic area difference constraints. Option B suggests a length of forty meters, failing to satisfy the simultaneous perimeter and area equations. Option D offers a length of sixty meters, which would improperly invert the area relationship with the square.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. In how many sequences can 7 players throw a ball such that the youngest player does not go last-.
Show answer Hide answer
Answer: C. 4320
Total unconstrained arrangements of seven players throwing a ball equal seven factorial or fifty zero forty. Arrangements where the youngest player is restricted to the final position equal six factorial or seven twenty....
Q2. A rectangle has a 60m perimeter. If its length is twice its breadth, what is its area__________?
Show answer Hide answer
Answer: C. 200m2
The perimeter of a rectangle is equal to twice the sum of its length and breadth. Given the perimeter is sixty meters and length is twice breadth, dimensions evaluate to twenty and ten. Multiplying length by breadth yiel...
Q3. A rectangle's length increases by 10% and breadth drops by 10%. What is the area of the resulting rectangle_________?
Show answer Hide answer
Answer: C. Decreased by 1%
Sequential percentage modifications to rectangle dimensions alter total area through compounded multiplicative scaling factors. Scaling length by a factor of one point one and breadth by zero point nine results in zero p...
Q4. A rhombus has a 68 cm perimeter and a 16 cm diagonal. Find its area.
Show answer Hide answer
Answer: B. 240 cm2
Dividing the rhombus perimeter of sixty eight centimeters by four gives a side length of seventeen centimeters. Applying the Pythagorean theorem to the half diagonals yields the other diagonal length of thirty centimeter...
Q5. What is the smallest four-digit integer that can be divided without remainder by 15, 25, 40, and 75_________?
Show answer Hide answer
Answer: C. 9600
The least common multiple of fifteen, twenty five, forty, and seventy five is calculated as six hundred. Dividing the smallest four digit number by six hundred identifies the lower bounding multiplier. Multiplying six hu...
Q6. Two squares have perimeters of 48 cm and 20 cm. Find the perimeter and diagonal of a square whose area equals their combined sum.
Show answer Hide answer
Answer: B. 13√2 cm
Combining the areas of the two smaller squares yields a total combined area of one hundred sixty-nine. Extracting the square root of one hundred sixty-nine determines the side length of the new square as thirteen. Multip...