Advertisements
Advertisements
प्रश्न
A footpath of uniform width runs all around the outside of a rectangular field 30 m long and 24 m wide. If the path occupies an area of 360 m2, find its width.
Advertisements
उत्तर
Let x be the width of the footpath.
Then
Area of footpath = `2 xx ( 30 + 24 )x + 4x^2`
= 4x2 + 108x
Again it is given that the area of the footpath is 360sq.m.
Hence,
4x2 + 108x = 360
x2 + 27x - 90 = 0
( x - 3 )( x + 30 ) = 0
x = 3
Hence width of the footpath is 3m.
APPEARS IN
संबंधित प्रश्न
A wire when bent in the form of a square encloses an area = 576 cm2. Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
The perimeter of a rhombus is 46 cm. If the height of the rhombus is 8 cm; find its area.
The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement
(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah.
The shaded region of the given diagram represents the lawn in the form of a house. On the three sides of the lawn, there are flowerbeds having a uniform width of 2 m.
(i) Find the length and the breadth of the lawn.
(ii) Hence, or otherwise, find the area of the flower-beds.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (0, 0), (p, 8), (6, 2) | 20 |
In the following, find the value of ‘a’ for which the given points are collinear
(a, 2 – 2a), (– a + 1, 2a) and (– 4 – a, 6 – 2a)
Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (– 4, – 2), (– 3, k), (3, – 2) and (2, 3)
When proving that a quadrilateral is a parallelogram by using slopes you must find
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is ______.
