The area of a rhombus is 60cm^2. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus.
area of a rhomus = (1/2)(product of its diagonals)
let the other diagonal be a
(1/2)(15a) = 60
15a= 120
a = 8
So let's find the hypotenuse of one of the right-angled triangles formed by the intersection of its diagonals
base = 4, height = 7.5
if h is the hypotenuse,
h^2 = 4^2 + 7.5^2
h = 8.5
so perimeter = 4(8.5) = 34 cm
34
7.5 is half the diagonal which was 15🤥thank me later
Where is 8.5 coming from
7.5 is from where?
Where 7.5
where 7.5 come from
To calculate the perimeter of the rhombus, we need to determine the length of one side. We can find this by using the diagonal length and the formula for the area of a rhombus.
The area of a rhombus is given by the formula: A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
In this case, we are given that the area of the rhombus is 60cm^2, and one of its diagonals is 15cm. Let's assume this diagonal is d1.
Using the formula for the area, we can rewrite it as: 60 = (15 * d2) / 2
Multiplying both sides of the equation by 2 gives us: 120 = 15 * d2
Dividing both sides of the equation by 15 gives us: d2 = 8
Now, we can use the formula for the perimeter of a rhombus, which states that the perimeter is equal to 4 times the length of one side. Let's assume this side length is s.
Therefore, s = d2 / 2 = 8 / 2 = 4
Finally, we can calculate the perimeter of the rhombus by multiplying the side length by 4: perimeter = 4 * s = 4 * 4 = 16 cm
So, the perimeter of the rhombus is 16 cm.