Question

The area of a rhombus is 72 cm square if the perimeter is 32 cm find its altitude

Answer 1

Solution :-

Let the side of the rhombus be 'a' cm

Perimeter of the rhombus = 32 cm

Also, Perimeter of the rhombus = 4a units

[ Where 'a' is the side of the rhombus ]

⇒ 32 = 4a

⇒ 32/4 = a

⇒ 8 = a

⇒ a = 8

Let the altitude of the rhombus be 'h'

Area of the rhombus = 72 cm²

Also, Area of the rhombus = a * h sq.units

[ Where 'a' is the side of the rhombus and 'h' is the altitude of the rhombus ]

⇒ 72 = 8 * h

⇒ 72/8 = h

⇒ 9 = h

⇒ h = 9

Therefore, the altitude of the rhombus is 9 cm .

Learn more :

Area of rhombus is 840 cm². if the perimeter of the rhombus is 148 cm, then find the sum of the length of its two diagonals.

https://brainly.in/question/14098613

Answer 2

$\huge{\mathfrak{\red {Question :}}}$

The area of a rhombus is 72 cm square, if the perimeter is 32 cm. Find its altitude.

$\huge{\mathfrak{\blue{Solution :}}}$

$\underline{\bold{Given}}$

• The area of the rhombus = $72\: cm^2$
• The perimeter of the rhombus = 32 cm

$\underline{\bold {To\: Find}}$

• The altitude of the rhombus.

$\boxed {\pink{Perimeter\:of\:rhombus=4\times side}}$

$\implies Perimeter = 4 \times side \\\implies 32 \: cm = 4 \times side \\\implies \frac{32}{4} \: cm = side \\\implies 8 \: cm = side \\\implies side = 8 \: cm$

$\boxed {\pink{Area\:of\:rhombus=Base\times Altitude}}$

$\implies Area = Base\times Altitude \\ \implies 72 \: cm^2 = 8 \: cm \times Altitude \\ \implies \frac{72cm^2}{8cm} = Altitude \\\implies 9 \: cm = Altitude \\ \implies Altitude = 9 \: cm$

$\green{\therefore{The \:altitude\: of\: the\: rhombus\: is\: 9 \:cm.}}$