Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let w be the width of the footpath.
Area of the path = Area of outer rectangle – Area of inner rectangle
∴ 208 = (32)(24) – (32 – 2w)(24 – 2w)
208 = 768 – 768 + 64w + 48w – 4w2
4w2 – 112w + 208 = 0
w2 – 28w + 52 = 0
w2 – 26w – 2w + 52 = 0
w(w – 26) – 2(w – 26) = 0
(w – 26)(w – 2) = 0
w = 26, 2
If w = 26, then breadth of inner rectangle = (24 – 52) m = –28 m, which is not possible.
Hence, the width of the footpath is 2 m.
APPEARS IN
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 sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:
- the value of x,
- the lengths of its sides,
- its area.
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.
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 farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.
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.
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 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 ______.
