The formula for the perimeter of an equilateral triangle is P = 3 × side.
Given P = 15 cm, solving 15 ÷ 3 = 5 cm.
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
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).
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
ND-21-5-2023
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
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
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
We need to calculate:
From trigonometric values:
0
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
The common difference is −3-3, so the sequence becomes: 18,15,12,9,6,318, 15, 12, 9, 6, 3 The 3rd mean is the 4th term: 9.
