The area of a rhombus is 84 sqm.,if its perimeter is 40 m. ,then find its altitude.
each side is 10 units
let the height be h
area of rhombus = base x height
10 x height = 84
height = 84/10 = 8.4
That's it.
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You are not going to believe how I "overthought" this question.
Here is what I did originally:
2 main properties we can use:
a rhomus has 4 equal sides
the diagonals of a rhomus right-bisect each other
let the diagonals have length 2a and 2b
the 4 triangles created are equal
so each triangle has area 21
so (1/2)ab = 21
ab = 42 ----> b = 42/a
also in each triangle, the hypotenuse is 10
a^2 + b^2 = 100
a^2 + 1764/a^2 = 100
a^4 - 100a^2 + 1764 = 0
I was expecting this to factor, but ....
a^2 = (100 ± √2944)/2
= 77.129... or 22.87...
a = √77.129 ... = 8.7823..
or
a = √22.87... = 4.7823..
if a = 8.7823.. , then b = 4.7823
if a = 4.7823.. , then b = 8.7823..
looks like we have "symmetrical" answers
and the long diagonal is 2(8.7823) = 17.56
the shorter diagonal is 2(4.7823) = 9.56
8.4
9m
To find the altitude of a rhombus, we need to know either the length of one side and the angle formed by two adjacent sides or the length of one diagonal. In this case, we are given the area and the perimeter of the rhombus, but we do not have any of the other required measurements.
Given the dimensions provided, we can calculate the side length of the rhombus using the perimeter.
Let's assume that the side length of the rhombus is 'a'.
Perimeter of a rhombus = 4 * side length
40 m = 4a
Dividing both sides of the equation by 4, we find:
a = 10 m
Now that we have the side length, we can use the formula to calculate the area of a rhombus:
Area of a rhombus = (Diagonal1 * Diagonal2) / 2
However, in this case, we are not given the lengths of the diagonals either. So, we need more information to find the altitude of the rhombus.
Please provide any additional information to proceed with finding the altitude.