Explanation

Let's denote the original length and width of the rectangle as L and W, respectively.

The original perimeter is:

2L + 2W = 34

If we increase the length by 2 cm, the new perimeter will be:

2(L + 2) + 2W

= 2L + 4 + 2W

The difference in perimeter is:

(2L + 4 + 2W) - (2L + 2W)

= 4

Explanation

If a² + b² = c², this follows the Pythagorean Theorem, which applies only to right-angled triangles.

Therefore, the triangle is a Right triangle, where c is the hypotenuse.

Explanation

The area of the sector can be calculated using the formula: Area = (θ/360) * πr², where θ is the central angle and r is the radius.

Given θ = 60° and r = 5 cm, we can substitute these values into the formula:

Area = (60/360) * π * (5)²

Area = (1/6) * π * 25

Area ≈ (1/6) * 3.14 * 25

Area ≈ 13.08 cm²

Explanation

To find the perimeter of the square-shaped field:

First, find the side length of the square:

Area = side²

2704 = side²

Take the square root:

side = √2704

side = 52

Now, find the perimeter:

Perimeter = 4 × side

= 4 × 52

= 208

Explanation

Explanation

When a quadratic polynomial (degree 2) is divided by a linear factor (degree 1), the quotient will have a degree one less than the original polynomial.

That means the result will be a linear polynomial (degree 1).

Explanation

The area of a rectangle is length × width:

Area = length × width

16 = 8 × width

Divide both sides by 8:

width = 2

The perimeter of a rectangle is 2 × (length + width):

Perimeter = 2 × (8 + 2)

= 2 × 10

= 20

Explanation

Step 1: Convert centimeters to meters

Since 1 meter = 100 centimeters, to convert centimeters to meters, we divide by 100.

Step 2: Calculate the length in meters

Length in meters = 250 cm / 100 = 2.5 m.

Explanation

Given the surface area of a sphere = 81π

The formula for surface area of a sphere is:

4πr² = 81π

Divide both sides by 4π:

r² = 81/4

r² = 20.25

r = √20.25

r = 4.5 m

Explanation

A sphere has one continuous curved surface with no edges or vertices.

Examples include a ball or a globe.