Explanation

To find the area of the carpeting part, we need to find the area of the inner rectangle (without carpet) and subtract it from the total area.

Length of inner rectangle = 7.8 - 22.3 = 3.2 m

Width of inner rectangle = 6.5 - 22.3 = 1.9 m

Area of the room = 7.8 * 6.5 = 50.7 m^2

Area of inner rectangle = 3.2 * 1.9 = 6.08 m^2

Area of carpet = Total area - Inner area

= 50.7 - 6.08

= 44.62 m^2

Explanation

We know:

- Angle of elevation (θ) = 60°

- Distance of the foot of the ladder from the wall (x) = 12.4 m

- We need to find the length of the ladder (hypotenuse)

Using the cosine function:
cos(θ) = adjacent side / hypotenuse
cos(60°) = 12.4 / hypotenuse
To find the hypotenuse (length of the ladder), we can rearrange the equation:
hypotenuse = 12.4 / cos(60°)
Using a calculator:
hypotenuse = 12.4 / 0.5
hypotenuse = 24.8
So, the length of the ladder is 24.8 meters.

Explanation

Explanation

Total grains = 10 + 100 + 1000 = 1110 grains.

Total length = 1110 × 0.9 = 999 cm.

Explanation

Given the volume of the cube-shaped pool is 10648 m³. To find the side length (s):

s³ = 10648

s = ∛10648

s = 22

The area of the base floor = s² = 22² = 484 m²

Cost = Area × Rate

= 484 × 85

= 41140

Explanation

The measure of the external angle of a regular hexagon is 60°.

This is because a hexagon has 6 sides, and the sum of the external angles of any polygon is always 360°, so 360° ÷ 6 = 60°.

Explanation

A cube has six equal square faces, each with the same dimensions.

All six faces of a cube are identical squares, making it a regular polyhedron.

Explanation

Given:

Radius (r) = 13 cm

Distance from center to chord (d) = 5 cm

Let's draw a perpendicular from the center to the chord. This will bisect the chord.

Using the Pythagorean theorem:

r² = d² + (half chord)²

13² = 5² + (half chord)²

169 = 25 + (half chord)²

(half chord)² = 169 - 25

= 144

half chord = √144

= 12 cm

Length of chord = 2 × half chord

= 2 × 12

= 24 cm

Explanation

Given:

Capacity = 50000 litres = 50 cubic meters (since 1 cubic meter = 1000 litres)

Length (l) = 2.5 m

Depth (h) = 10 m

Let's use the formula for the volume of a cuboid:

Volume = length × breadth × height

50 = 2.5 × breadth × 10

Now, solve for breadth (b):

50 = 25b

b = 50/25

b = 2 m

Explanation

Supplementary angles sum to 180 degrees:

(2x + 10) + (x + 20) = 180

Combine like terms:

3x + 30 = 180

Subtract 30:

3x = 150

Divide by 3:

x = 50