Question

The sides of a parallelogram are in the ratio 4:7. If its perimeter is 66cm .find the length of the sides .consider the following parellogram.

Answer 1

Answer:

The lengths of all the sides of parallelogram are AB = DC = 42 cm and AD = BC = 24 cm.

Let the parallelogram be denoted by ABCD.

It is given that the two adjacent sides of the parallelogram are in the ratio 4:7.

Also it is supplied that the perimeter of the parallelogram is 132cm.

If we consider the common multiple to be 'x', then we get the adjacent sides, AD and DC are:

AD = 4x cm

DC = 7x cm

As the opposite sides of a parallelogram are equal so, we get

BC = AD = 4x and

AB = DC = 7x

So,

Perimeter of the parallelogram is given by sum of total sides which is:

AB + BC + DC + AD =

= 7x + 4x + 7x + 4x

= 22x

We know total perimeter = 132 xm

∴ 22x = 132

⇒x = 132/22

⇒x = 6

So, the sides are

AB = 7x = 7×6 = 42 cm

BC = 4x = 4×6 =  24 cm

DC = 7x = 7×6 = 42 cm

AD = 4x = 4×6 = 24 cm

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Answer 2

✯✯ QUESTION ✯✯

The sides of a parallelogram are in the ratio 4:7. If its perimeter is 66cm .find the length of the sides .consider the following parellogram...

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\implies\tt{AB=DC=4x}$

$\implies\tt{BC=AD=7x}$

$\implies\tt{Perimeter=132cm}$

➥A.T.Q : -

$\implies\tt{AB+BC+CD+AD=132}$

$\implies\tt{4x+7x+4x+7x=132}$

$\implies\tt{22x=132}$

$\implies\tt{x=\cancel\dfrac{132}{22}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{6}}}$

➥Now ,

$\implies\tt{AB=4(6)}$

$\implies\tt\bold{24cm}$

$\implies\tt{BC=7(6)}$

$\implies\tt\bold{42cm}$

$\implies\tt{CD=4(6)}$

$\implies\tt\bold{24cm}$

$\implies\tt{AD=7(6)}$

$\implies\tt\bold{42cm}$

_______________________

✔VERIFICATION : -

$\implies\tt{24+42+24+42=132}$

$\implies\tt{132=132}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\purple{L.H.S}\orange{=}\green{R.H.S}}}$

_______________________

☛Properties of Parallelogram : -

★Opposite sides are parallel..

★Diagonals bisect each other..

★Opposite angles are congruent.