Question

Диагонали ромба относятся как 3:4 а его площадь равна 216 кв см найдите периметр ромба

Answer 1

Ответ:

60 см

Объяснение:

Пусть одна диагональ ромба = 3x, вторая = 4x, тогда

S = 1 / 2 * d₁ * d₂ = 1 / 2 * 3x * 4x = 216 см²

6x² = 216 см²

x² = 36 см²

x = 6 см

Первая диагональ = 3 * 6 = 18 см

Вторая = 4 * 6 = 24 см

Найдём сторону ромба по теореме Пифагора (через прямоугольный треугольник с катетами 9 см и 12 см):

a = √(81 + 144) = √225 = 15 см

P = 4a = 15 * 4 = 60 см

Answer 2

Объяснение:

Диагональ d1=3x

Диагональ d2=4x

S=216 cм^2

S=(d1×d2)/2

216×2=3X×4X

432=12X^2

X^2=432:12

X^2=36

X=6

d1=3×6=18 см

d2=4×6=24 см

Р=4а

а-сторона ромба

По теореме Пифагора :

а=корень ((d1/2)^2+(d2/2)^2)=

=корень ((18/2)^2+(24/2)^2)=

=корень (9^2+12^2)=корень 225=15 см

Р=4×15=60 см

Ответ : 60 см

Answer 3

Finding the Perimeter of a Rhombus with Given Diagonal Ratio and Area

To find the perimeter of a rhombus when the ratio of its diagonals is 3:4 and its area is 216 sq cm, we can use the following steps:

1. Calculate the Length of Diagonals: - Let's assume the length of the shorter diagonal is 3x and the longer diagonal is 4x. - The area of a rhombus can be calculated using the formula: Area = (1/2) * d1 * d2, where d1 and d2 are the diagonals. - We know the area is 216 sq cm, so we can use this information to find the value of x.

2. Find the Perimeter: - Once we have the lengths of the diagonals, we can use them to find the perimeter of the rhombus.

Let's proceed with the calculations.

Calculations

1. Calculate the Length of Diagonals: - Using the area formula, we can find the value of x: - Area = (1/2) * d1 * d2 - 216 = (1/2) * 3x * 4x - 216 = 6x^2 - x^2 = 36 - x = 6

- So, the length of the shorter diagonal (3x) is 18 cm, and the length of the longer diagonal (4x) is 24 cm.

2. Find the Perimeter: - The perimeter of a rhombus can be calculated using the formula: Perimeter = 4 * side length. - To find the side length, we can use the Pythagorean theorem: side length = sqrt((d1/2)^2 + (d2/2)^2).

- For the given diagonals: - Side length = sqrt((18/2)^2 + (24/2)^2) - Side length = sqrt(81 + 144) - Side length = sqrt(225) - Side length = 15 cm

- Perimeter = 4 * 15 - Perimeter = 60 cm

So, the perimeter of the rhombus is 60 cm.