The area of a rhombus is 96 cm square . if its perimeter is 32 cm , find its altitude?
- Posted:
- 3+ months ago by nithya go...
- Topics:
- square, area, perimeter, altitude
Responses (2)
A = base * altitude
we don't know the base, we can find the length of the base from the perimeter, perimeter is the sum of the lengths of the sides, the sides of a rhombus are equal
perimeter = 4 * length of one side
32 cm = 4 * length of one side
divide both sides by 4
32 cm / 4 = (4 * length of one side) / 4
8cm = length of one side
common sense, the base is equal to 8 cm
A = base * altitude
96 = 8 * altitude
divide both sides by 8
12 cm = altitude
A rhombus has 4 equally long sides s.
The perimeter p of our rhombus is 32 cm, thus
s = 32 / 4 = 8 cm.
Even if the rhombus were a square (a special rhombus with equal inner angles of 90°),
the area a would be
a = s² = 64 cm².
That's the maximum area for a closed shape with constant p in a Euclidean plane made of four straight lines and four corners (vertices).
There is no way to get to 96 cm².