Question

One side of parallelogram is 3/4 times
of its adjecent side if the perimeter of
parallelogram.
Parallelogram is 70cm find the sides of parallelogram​

Answer 1

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

$\:\:$

$\large\underline{\green{\bf Given :-}}$

$\:\:$

• One side of parallelogram is 3/4 times of its adjacent side

$\:\:$

• Perimeter of parallelogram is 70cm

$\:\:$

$\large\underline{\red{\bf To \: Find :-}}$

$\:\:$

• Sides of parallelogram

$\:\:$

$\large\underline{\orange{\bf Solution :-}}$

$\:\:$

• Let one side of parallelogram be "l"

• Let the adjacent side be "b"

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

One side of parallelogram is 3/4 times of its adjacent side

$\:\:$

➜ $\sf b = \dfrac { 3 } { 4 } × l$ ⚊⚊⚊⚊ ⓵

$\:\:$

$\underline{\bold{\texttt{Perimeter of parallelogram :}}}$

$\:\:$

➠ 2(Length + Breadth) ⚊⚊⚊⚊ ⓶

$\:\:$

$\underline{\bold{\texttt{Perimeter of given parallelogram :}}}$

$\:\:$

• Length = l

• Breadth = b

• Perimeter = 70

$\:\:$

⟮ Putting these values in ⓶ ⟯

$\:\:$

➜ 2(l + b) = 70

$\:\:$

➜ $\sf l + b = \dfrac { 70 } { 2 }$

$\:\:$

➜ l + b = 35 ⚊⚊⚊⚊ ⓷

$\:\:$

⟮ Putting $\sf b = \dfrac { 3 } { 4 } × l$ from ⓵ to ⓷ ⟯

$\:\:$

➜ l + b = 35

$\:\:$

➜ $\sf l + \dfrac { 3 } { 4 } × l = 35$

$\:\:$

➜ $\sf \dfrac { 4l + 3l } { 4 } = 35$

$\:\:$

➜ $\sf \dfrac { \cancel 7l } { 4 } = \cancel { 35}$

$\:\:$

➜ $\sf \dfrac { l } { 4 } = \cancel { 5}$

$\:\:$

➨ l = 20 ⚊⚊⚊⚊ ⓸

$\:\:$

• Hence one side of parallelogram is 20 cm

$\:\:$

⟮ Putting l = 20 from ⓸ to ⓷ ⟯

$\:\:$

➜ l + b = 35

$\:\:$

➜ 20 + b = 35

$\:\:$

➜ b = 35 - 20

$\:\:$

➨ b = 15

$\:\:$

• Hence the adjacent side is of length 15 cm

$\:\:$

We know that opposite sides of parallelogram are equal hence the other two sides are 20 cm and 15 cm too

$\:\:$

∴ The sides of parallelogram are 20 cm , 15 cm , 20 cm , 15 cm

$\:\:$

━━━━━━━━━━━━━━━━━━━━━━━━━

Additional information

$\:\:$

Area of parallelogram

$\:\:$

• A = b × h

$\:\:$

Where,

$\:\:$

➻ A = Area

➻ b = Base

➻ h = Height

$\:\:$

Properties of parallelogram

$\:\:$

• Opposite sides are congruent

• Opposite angels are congruent

• Consecutive angles are supplementary

• If one angle is right, then all angles are right.

• The diagonals of a parallelogram bisect each other.

• Each diagonal of a parallelogram separates it into two congruent triangles

$\:\:$

═════════════════════════