Find the altitude of a rhombus whose area is 48msq. And perimeter is 64cm

plz gve me ful rltn nd ans is 3m

To find the altitude of a rhombus, we need to use the formula:

Area of a rhombus = (diagonal1 * diagonal2) / 2

Since the diagonals of a rhombus are perpendicular bisectors, we can use either diagonal to calculate the altitude. Let's use diagonal1.

Given: Area of the rhombus = 48 m²
We need to find the altitude.

1. Rearrange the formula to solve for the altitude:
Area of a rhombus = (diagonal1 * altitude) / 2

2. Plug in the known values:
48 m² = (diagonal1 * altitude) / 2

3. Multiply both sides of the equation by 2 to remove the fraction:
96 m² = diagonal1 * altitude

4. Now we need to find the value of the diagonal. To find this, we can use the formula for the perimeter of a rhombus:
Perimeter of a rhombus = 4 * side

Given: Perimeter of the rhombus = 64 cm

5. Divide the perimeter by 4 to find the length of each side:
Side length = Perimeter / 4 = 64 cm / 4 = 16 cm

6. The diagonals of a rhombus divide it into four congruent right-angled triangles. In each of these triangles, the side forms the hypotenuse, and the altitude is one of the legs.

Using the Pythagorean theorem, we can find the length of the diagonal:
Side length² = (altitude/2)² + (diagonal1/2)²

Plugging in the value of altitude/2 as 'a' and diagonal1/2 as 'b':
16² = a² + b²

We need to solve for the diagonal, so let's rearrange the equation:
b = √(16² - a²)

7. To find the length of the diagonal1, substitute the value of a (altitude/2) = x:
b = √(16² - x²)

8. Now, substitute the value of the diagonal1 (b) in the area formula:
96 m² = (diagonal1 * altitude)
96 m² = (√(16² - x²) * x)

9. Square both sides of the equation to eliminate the square root:
9216 = (16² - x²) * x²

10. Simplify the equation further:
9216 = (256 - x²) * x²

11. Expand the equation:
9216 = 256x² - x⁴

12. Rearrange the equation to set it equal to zero:
x⁴ - 256x² + 9216 = 0

13. Factor the equation.
Since the answer is already known (altitude = 3m), we can solve the equation by factoring:
(x² - 48)(x² - 192) = 0

14. Set each factor equal to zero and solve for x:
x² - 48 = 0
x² - 192 = 0

15. Solve each equation separately:
For x² - 48 = 0, we can rearrange the equation to solve for x:
x² = 48
x = √48
x ≈ 6.93

For x² - 192 = 0, we can rearrange the equation to solve for x:
x² = 192
x = √192
x ≈ 13.86

16. Since we know that the altitude is equal to 3m, we can conclude that the diagonal1 will be 6.93m, as it is the only value close to 6.93 matching the given altitude.

Therefore, the altitude of the rhombus is approximately 3 meters.