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
Explanation
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 yields the exact side length of twenty centimeters. Area of a square is calculated by squaring the length of its side variable. Area of a rectangle is determined by multiplying its measured length by its breadth. Algebraic substitution allows comparing geometric properties of different shapes using single variable equations.
Architects frequently compare floor plan areas to optimize room dimensions and material usage. Geometric scaling principles help designers resize components while maintaining specific proportional area relationships. Calculations involving multiple geometric figures are essential in construction and manufacturing industries. Option A suggests fifteen centimeters which generates an incorrect ratio when testing area conditions. Option C suggests thirty centimeters which produces an area too large for the given parameters. Option D suggests sixty centimeters which violates the proportional dimensional limits established initially.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the altitude of an equilateral triangle whose side measures 2√3 cm_________?
Show answer Hide answer
Answer: D. 3 cm
The altitude formula for an equilateral triangle multiplies the side length by the square root of three over two. Substituting the side length of two times the square root of three simplifies the expression directly. Mul...
Q2. How much water in ml must be added to dilute 9 ml of a 50% alcohol lotion down to 30% alcohol__________?
Show answer Hide answer
Answer: D. 6
Applying the standard dilution formula initial concentration times initial volume equals final concentration times final volume. Multiplying fifty percentage by nine milliliters gives four hundred fifty concentration vol...
Q3. Determine the cash required to acquire Rs. 3200 of a 7(1/2)% stock at 107 with a (1/2)% brokerage fee.
Show answer Hide answer
Answer: A. 3440
The purchase price percentage and brokerage fee are combined to find the effective cost multiplier. Multiplying the stock nominal value by the total cost factor yields the exact required cash amount. Accurate computation...
Q4. 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...
Q5. A square field has an area of 3136 sq m. What is the total cost of fencing it with barbed wire 3 m away at Rs. 1.50 per meter, leaving two 1 m wide entrances?
Show answer Hide answer
Answer: C. Rs.999
The square field area of thirty-one thirty-six square meters means its side length is fifty-six meters. Fencing placed three meters away adds six meters to each dimension, resulting in a fence perimeter of two hundred fo...
Q6. 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
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 mis...