Question

find the altitude of rhombus whose area is 22.4 cm² and perimeter is 16

Answer 1

$\bold{\underline{\underline{Answer:}}}$

Altitude of the rhombus is 5.6 cm

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• Area of rhombus = 22.4 cm²
• Perimeter of rhombus = 16 cm

To find :

• Altitude of the rhombus

Solution :

Using the formula for perimeter of the rhombus we can find the length of side.

Formula :-

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

Let side of the rhombus be x.

Block in the values,

$\bold{16=4\times\:x}$

$\bold{\dfrac{16}{4}}$ = x

$\bold{4=x}$

•°• Side of the rhombus = 4 cm

We can know use the formula for area of the rhombus and calculate the altitude.

$\bold{\boxed{\green{\sf{Area\:of\:rhombus\:=\:base\times\:altitude}}}}$

Base = x

Altitude = h

Block in the values,

$\bold{22.4=x\times\:h}$

$\bold{22.4=4\times\:h}$

$\bold{\dfrac{22.4}{4}}$ = h

$\bold{5.6}$ = h

•°• Altitude of the rhombus = 5.6 cm

Answer 2

$\huge\bf{Answer:}$

Given:

$\sf{Perimeter \:of \:rhombus = 16cm}$

$\sf{Area\: of \:rhombus = 22.4cm^2}$

To find:

$\sf{Altitude\: of \:rhombus = h}$

Solution:

$\sf{We \:know \:that \:all \:sides\: of\: rhombus \:is \:equal.}$

$\sf{Therefore, \:side\: of\: rhombus}$

$=\frac{perimeter}{4} =\frac{16}{4}=4cm$

$\sf{We \:know\: that \:area \:of\: rhombus \:is\: the}$$\sf{product \:of\: its \:base\: and \:height as\: rhombus}$$\sf{too \:is\: a\: parallelogram.}$

$area = base \times height \\ 22.4 = side \times altitude \\ 22.4 = 4 \times h \\ h = \frac{22.4}{4}$

$\boxed{h = 5.6cm}$

@ItsMysteriousGirl✒️