Advertisements
Advertisements
प्रश्न
The area of a big rectangular room is 300 m2. If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.
Advertisements
उत्तर
Let the original length and breadth of the rectangular room be x m and y m respectively.
Area of the rectangular room = xy = 300
`=> y = 300/x` ...(1)
New length = (x – 5) m
New breadth = (y + 5) m
New area = (x – 5)(y + 5) = 300 ...(Given)
Using (1), we have:
`(x - 5)(300/x + 5) = 300`
`300 + 5x - 1500/x - 25 = 300`
`5x - 1500/x - 25 = 0`
`5x^2 - 25x - 1500 = 0`
`x^2 - 5x - 300 = 0`
`x^2 - 20x + 15x - 300 = 0`
`x(x - 20) + 15(x - 20) = 0`
`(x - 20)(x + 15) = 0`
x = 20, –15
But, x cannot be negative.
So, x = 20.
Thus, the length of the room is 20 m.
संबंधित प्रश्न
The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.
The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.
A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m2, find the width of the footpath.
Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
The dimensions of a rectangular field are 50 m and 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square metre, respectively, is Rs. 52,000. Find the width of the gravel path.
A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is `7/8` that of the lawn, find the dimensions of the lawn.
The perimeter of a square is numerically equal to its area. The perimeter of the square is ______.
If the width of the uniform shaded portion of x m; its area in terms of x is ______.
The length of a rectangle is 3 m more than its width. If its area is 180 m2; the length of the rectangle is ______.
