Explanation

The formula for the perimeter of an equilateral triangle is P = 3 × side.

Given P = 15 cm, solving 15 ÷ 3 = 5 cm.

Explanation

Since it's a square garden, all sides are equal. To find the length of one side, take the square root of the area:

√2704 m² = 52 m

Explanation

When rotating a point (x, y) 270° clockwise, the new coordinates are (y, -x).

For P(2, -9), the new coordinates P' will be (-9, -2).

Explanation

The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h);

where 'b' is the base

and 'h' is the height of the triangle

Explanation

The formula relating arc length (l), radius (r), and central angle (θ) is:

l = rθ

Given:

l = 45 cm

r = 9 cm

θ = l / r

= 45 / 9

= 5 radians

Explanation

To find the area of the path, we need to find the area of the larger rectangle and subtract the area of the smaller rectangle.

Area of larger rectangle = Length × Width

= 60 × 40

= 2400 m²

Length of inner rectangle = 60 - 2 × 2.5 = 55 m

Width of inner rectangle = 40 - 2 × 2.5 = 35 m

Area of inner rectangle = 55 × 35

= 1925 m²

Area of path = Area of larger rectangle - Area of inner rectangle

= 2400 - 1925

= 475 m²

Explanation

The formula to find the arc length (I) is:

I = rθ

Given values:

I = 30 cm

r = 6 cm

Rearrange the formula to solve for θ:

θ = I / r

= 30 / 6

= 5 radians

Explanation

 We need to calculate:

Step 1: Find the Values

From trigonometric values:

• sin90∘=1
• cos90∘=0

Step 2: Multiply

Final Answer:

0

Explanation

Given:

Side of square = 1200 cm

Width of strip = 10 cm

Side of larger square (including strip) = 1200 + 2(10)

= 1200 + 20

= 1220 cm

Area of larger square = 1220² = 1488400 cm²

Area of square = 1200² = 1440000 cm²

Area of strip = Area of larger square - Area of square

= 1488400 - 1440000

= 48400 cm²

Explanation

The common difference is $-3$, so the sequence becomes:
$18, 15, 12, 9, 6, 3$
The 3rd mean is the 4th term: 9.