Question

Area of a rhombus is 72 sqcm .If its perimetre is 36cm.Find its altitude

Answer 1

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
36 cm = 4 * length of one side
divide both sides by 4
36 cm / 4 = (4 * length of one side) / 4
9cm = length of one side

common sense, the base is equal to 9 cm

A = base * altitude
72 = 9 * altitude
divide both sides by 9
8cm = altitude

Answer 2

The altitude of a rhombus (h) = 8 cm

Step-by-step explanation:

Given,

The area of a rhombus = 72 $cm^{2}$ and

The perimeter of a rhombus = 36 cm

To find, the altitude of a rhombus (h) = ?

We know that,

The perimeter of a rhombus = 4 × Side(a)

⇒ 4 × Side(a) = 36 cm

⇒ a = $\dfrac{36}{4}$ cm = 9 cm

∴ The base of rhombus = 9 cm

The area of a rhombus = Base × altitude

⇒ 9 cm × h = 72 $cm^{2}$

⇒ h = 8 cm

Thus, the altitude of a rhombus (h) = 8 cm