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The length of a rectangle wall is 3/2 times of its height. If the area of the wall is 600m². What is the sum of the length and height of the wall?
length = 2x
height = 3x
Area of the wall = 3x * 2x = 6x² = 600
x = 10; Sum of the length and height of the wall = 50
If the area of a circle is 616cm² whose diameter is equal to radius of a semicircle. Find the perimeter of the semicircle?
Area of a circle = 616cm²
πr² = 616; r = 14
D = Radius of Semi Circle = 28
Perimeter of the semicircle = πr + 2r = 144cm
One side of rectangular ground is 8m and its diagonal is 17m. Find the area of ground?
d = √(l² + b²)
17 = √(l² + 8²)
l² = 17² – 8² ⇒ l = 289 – 64 = 225
l = 15 Area = 15 * 8 = 120m²
The side of a square shaped garden is 8√2 . Find the maximum possible distancce between any two corners
d = a√2
a = 8√2
d = 16m
A rectangular ground 16m long and 10m breadth. It has a gravel path 2.5m wide all around it on the outside. What is the area of the path?
Area of ground = 16 * 10 = 160
Total area (ground + path) = (16 + 5)*(10 + 5) = 315
Area of path = 315 – 160 = 155 m²
If the side of the square is increased by 30%, then how much % does its area get increased?
Area of the plot = 1.3 * 1.3 = 1.69 = 69%
A ladder is resting with one end in contact with the top of the wall of height 15m and the other end of the ground is at a distance 8m from the wall. The length of the ladder is?
Hypotenuse = √(base)² + (altitude)²
√(8)² + (15)² = √289 = 17m
The perimeter of a square is equal to twice the perimeter of a rectangle of length 10 cm and breadth 4 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square?
Perimeter of square = 2(l + b)
= 2 * 2(10 + 4) = 2 * 28 = 56 cm
Side of square = 56/4 = 14 cm
Radius of semi circle = 14/2 = 7cm
Circumference of the semicircle = 22/7 * 7 + 14 = 36 cm
The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
Circumference of the circle = 132
2πR = 132; R = 21 cm
Side of square = 21 cm
Length of the rectangle = 3/5 * 21 = 63/5
Area of the rectangle = 63/5 * 15 = 189 cm²
Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?
Side of square = 72/4 = 18 cm
Smallest side of the right angled triangle = 18 – 13 = 5 cm
Length of rectangle = 112/8 = 14 cm
Second side of the right angled triangle = 14 – 2 = 12 cm
Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?
[3x + 4 / 2x + 4] = 10/7
x = 12
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 144 = 864m²
The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 500 cm. If the area of the rectangle is less than that of a Square then find the area of the rectangle?
Perimeter of rectangle = Perimeter of Square = 160
4a = 160 ⇒ a = 40 Area of square = 1600
1600 – lb = 500
lb = 1100 cm²
Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 441 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?
Area = 441 cm²
a = 21 cm
Perimeter of Square = 4 * 21
Circumference of a Circle = 4 * 21 * 22/7
2πr = 4 * 3 * 22
r = 12 * 22 * 7 / 2 * 22 = 42 cm
Radius of Circle B = 42/4 = 10.5 cm
Area of Circle = πr² = 22/7 * 10.5 * 10.5 = 346.5 cm²
The area of a rectangle is equal to the area of a square whose diagonal is 12√2 metre. The difference between the length and the breadth of the rectangle is 7 metre. What is the perimeter of rectangle ? (in metre).
d = a√2
12√2 = a√2
a = 12
l * b = a² = (12²) = 144
l – b = 7 ; l = b + 7
(b + 7)*(b) = 144
b² + 7b – 144 = 0
b = 9; l = 16
2(l + b) = 2(16 + 9) = 50m
The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the area of the rectangle?
Length = x; Breadth =y
xy – (x5)(y+3) = 9
3x – 5y – 6 = 0 —(i)
(x+3)(y+2) – xy = 67
2x + 3y 61 = 0 —(ii)
solving (i) and (ii)
x = 17m ; y = 9m
Area of the Rectangle = 153 m
The length of a plot is four times its breath. A playground measuring 900 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?
Area of the plot = (4 x 900) m²
= 3600 m²
Breadth = y meter
Length = 4y meter
Now area = 4y x y = 3600 m²
⇒ y² = 900 m²
⇒ y = 30 m
∴ Length of plot = 4y =120 m
The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the radius and height of the cylinder?(in m)
r + h = 19 m
2πr(r + h) = 1672
r = 1672 * 7/ 2 * 22 * 19 = 14
r = 14 ; h = 5
If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?
(x+20) / x = 5 / 3
3x + 60 = 5x
x = 30m; Area = 900m²
The length of a park is four times of its breadth. A playground whose area is 1024 m² covers 1/4th part of the park. The length of the park is?
l = 4b
Area of the park = 4 * 1024 m²
l * b = 4 * 1024
l * l/4 = 4 * 4 * 1024
l² = 1024 * 16; l = 32 * 4 = 128 m
The width of a rectangular piece of land is 1/4 th of its length. If the perimeter of the piece of land is 320 m its length is?
length = l ; breadth = l/4
2(l + b) = 320
2(l + l/4) = 320
l = 320 * 4/10 = 128m
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