# The area of a rhombus is 96 cm square . if its perimeter is 32 cm , find its altitude?

 Respond to this Question Report Mark as Favorite

## 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.