Question

the area of rhombus is 102 cm square. if it's perimeter is 24 cm, find it's altitude.​

Answer 1

Answer:

Here, the concept of area and perimeter of rhombus has been used. We see that we're given with area of rhombus and it's perimeter and we are asked to find it's altitude. In order to find it's altitude, we will firstly find it's side by perimeter of parallelogram formula since, rhombus is also an parallelogram. After finding it's side we will calculate it's height by putting all the values in area of parallelogram formula.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Formula used:

$\bullet\;\boxed{\sf{Perimeter\: of\: rhombus\:=\:}\bold{4\times side}}$

$\bullet\;\boxed{\sf{Area\:of\: parallelogram\: =\:}\bold{base\times height}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Solution:

Given,

» Perimeter of rhombus = P = 24 cm

» Area of rhombus = A = 102 cm²

• Let the side of rhombus be x cm.
• Let the height of rhombus be h cm.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

~For side of rhombus ::

We know that,

$\\\qquad\longrightarrow\quad\tt{Perimeter\; of\; rhombus=Side\times 4}$

$\\\qquad\longrightarrow\quad\tt{24=x\times 4}$

$\\\qquad\longrightarrow\quad\tt{x=\dfrac{24}{4}}$

$\\\qquad\longrightarrow\quad\tt{x=6\; cm}$

We've calculated the side of rhombus that is 6 cm. Now, equating this value in area of rhombus formula. We know, the rhombus is also an parallelogram. So we can say that area of rhombus equals to area of parallelogram so,

$\\\qquad\dashrightarrow\quad\tt{Area\; of\; rhombus=Base\times height}$

$\\\qquad\dashrightarrow\quad\tt{102=6\times h}$

$\\\qquad\dashrightarrow\quad\tt{h=\dfrac{102}{6}}$

$\\\qquad\dashrightarrow\quad\underline{\boxed{\tt{height=\bold{\purple{17\; cm}}}}}$

Therefore, the required answer is:

❝The height of rhombus is 17 cm.❞