Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The area of the square is 484.
Let a be the length of each side of the square.
Now
a2 = 484
a = 22 m
Hence, the length of the wire is = 4 × 22 = 88 m.
(i) Now, this 88 m wire is bent in the form of an equilateral triangle.
Side of the triangle = `88/3`
= 29.3 m
Area of the triangle = `sqrt3/4` × (Side)2
= `sqrt3/4` × (29.3)2
= 372.58 m2
(ii) Let x be the breadth of the rectangle.
Now,
2(l + b) = 88
16 + x = 44
x = 28 m
Hence, area = 16 × 28 = 448 m2.
APPEARS IN
संबंधित प्रश्न
ABCD is a square with each side 12 cm. P is a point on BC such that area of ΔABP: area of trapezium APCD = 1: 5. Find the length of CP.
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
A rectangular plot 85 m long and 60 m broad is to be covered with grass leaving 5 m all around. Find the area to be laid with grass.
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.
The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.
Two adjacent sides of a parallelogram are 28 cm and 26 cm. If one diagonal of it is 30 cm long; find the area of the parallelogram. Also, find the distance between its shorter sides.
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.
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (p, p), (5, 6), (5, –2) | 32 |
Let P(11, 7), Q(13.5, 4) and R(9.5, 4) be the midpoints of the sides AB, BC and AC respectively of ∆ABC. Find the coordinates of the vertices A, B and C. Hence find the area of ∆ABC and compare this with area of ∆PQR.
