Question

Ratio of the adjacent sides of a parallelogram is 4:5 and it's perimeter is 360 cm. Find the length of each of its side

Answer 1

Answer✓

Sides are:-

• AB=80Cm
• BC=100Cm
• CD=80Cm
• AD=100Cm

To find:

Sides of Parellelogram

Given:

Perimeter=360cm

Assumption:

Let ratio of adjacent sides be 4x:5x

Solution:

In Parellelogram opposite sides are equal so:-

$\sf AB=CD = 4x\\\\ \sf BC=AD = 5x$

Perimeter of Parellelogram=sum of all sides

360cm=AB+BC+CD+AD

$\sf 360cm = 4x + 5x + 4x + 5x \\ \\ \sf360cm = 18x \\ \\ \sf \frac{360}{18} = x \\ \\ \sf20cm = x$

$\sf \: so \: sides \: are : - \\ \\ \sf: \implies AB = 4x = 80cm \\ \sf: \implies BC = 5x = 100cm \\ \sf : \implies CD =4x = 80cm \\ \sf: \implies AD = 5x = 100cm$

Verification:

Perimeter=sum of all sides

360cm=AB+BC+CD+AD

360cm=80cm+100cm+80cm+100cm

360cm=360cm

$\sf \boxed{ \large { \blue{LHS=RHS}}}$

Answer 2

Answer:

Answer✓

Sides are:-

AB=80Cm

BC=100Cm

CD=80Cm

AD=100Cm

To find:

Sides of Parellelogram

Given:

Perimeter=360cm

Assumption:

Let ratio of adjacent sides be 4x:5x

Solution:

In Parellelogram opposite sides are equal so:-

\begin{gathered} \sf AB=CD = 4x\\\\ \sf BC=AD = 5x\end{gathered}

AB=CD=4x

BC=AD=5x

Perimeter of Parellelogram=sum of all sides

360cm=AB+BC+CD+AD

\begin{gathered} \sf 360cm = 4x + 5x + 4x + 5x \\ \\ \sf360cm = 18x \\ \\ \sf \frac{360}{18} = x \\ \\ \sf20cm = x\end{gathered}

360cm=4x+5x+4x+5x

360cm=18x

18

360

=x

20cm=x

\begin{gathered}\sf \: so \: sides \: are : - \\ \\ \sf: \implies AB = 4x = 80cm \\ \sf: \implies BC = 5x = 100cm \\ \sf : \implies CD =4x = 80cm \\ \sf: \implies AD = 5x = 100cm \\ \\ \\ \\ \\ \\ \end{gathered}

sosidesare:−

:⟹AB=4x=80cm

:⟹BC=5x=100cm

:⟹CD=4x=80cm

:⟹AD=5x=100cm

Verification:

Perimeter=sum of all sides

360cm=AB+BC+CD+AD

360cm=80cm+100cm+80cm+100cm

360cm=360cm