Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the side of the square lawn be x m.
Area of the square lawn = x2 m2
The square lawn is bounded on three sides by a path which is 4 m wide.
Area of outer rectangle = (x + 4)(x + 8) = x2 + 12x + 32
Area of path = x2 + 12x + 32 – x2 = 12x + 32
From the given information, we have:
`12x + 32 = 7/8 x^2`
`96x + 256 = 7x^2`
`7x^2 - 96x - 256 = 0`
`7x^2 - 112x + 16x - 256 = 0`
`7x(x - 16) + 16(7x + 16) = 0`
`(x - 16)(7x + 16) = 0`
`x = 16, (-16)/7`
Since, x cannot be negative.
So, x = 16 m.
Thus, each side of the square lawn is 16 m.
संबंधित प्रश्न
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.
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.
An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same area. Find the size of the larger tiles.
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.
A car made a run of 390 km in ‘x’ hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find ‘x’.
The perimeter of a rectangular field is 28 m and its area is 40 sq. m. Its sides are ______.
The area of the given rectangle is 60 sq. m and its longer side is 10 m, the perimeter of the rectangle 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 ______.
