Question

one side of a parallelogram are is 3/4 time its adjacent side. if the perimeter is 110 cm.find the sides of the parallelogram.​

Answer 1

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• One side of a parallelogram is ¾ times the adjacent side .
• The perimeter of the parallelogram is 110 cm.

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• The sides of the parallelogram.

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

We know that the opposite sides of a parallelogram are equal . So , let us take one side be x .

And given that other side of the parallelogram is 3/4 times the adjacent side . So the side will be 3x/4 .

$\tt \green{\leadsto \mathscr{A}ccording\:to\:\mathscr{Q}usetion:-}$

$\tt:\implies Perimeter_{parallelogram}=2(side_1+side_2)$

$\tt:\implies 110cm=x+x+\dfrac{3x}{4}+\dfrac{3x}{4}$

$\tt:\implies 110cm=2x+\cancel2\times\bigg\lgroup \dfrac{3x}{\cancel4}\bigg\rgroup$

$\tt:\implies 110cm=2x+\dfrac{3x}{2}$

$\tt:\implies 110cm=\bigg\lgroup\dfrac{4x+3x}{2}\bigg\rgroup$

$\tt:\implies 110cm=\dfrac{7x}{2}$

$\tt:\implies x=\dfrac{110cm\times2}{7}$

$\tt:\implies x=\dfrac{220cm}{7}$

$\tt:\implies x=\dfrac{22}{7}\times10$

$\tt:\implies x=\pi \times10$

$\underline{\boxed{\red{\tt{\longmapsto \:\:x=\:\:10\pi cm}}}}$

$\bf Hence\; the\:sides\;will\;be:$

• $\orange{\boxed{\tt\pink{\dag}\purple{First\:side\:=\:x\:=\:10\pi cm}}}$

• $\orange{\boxed{\tt\pink{\dag}\purple{Second\:side\:=\:\dfrac{3x}{4}\:=\:7.5\pi cm}}}$

Answer 2

Answer:

Adjacent sides are 31.42 cm and 23.55 cm

Step-by-step explanation:

Let adjacent side be x

One side = 3/4 of x = 3x / 4

Perimeter = 2(l+b)

P = 2 ( x + 3x/4)

P = 2 (4x + 3x/4)

P = 2(7x/4)

P = 14x/4

Substituting P = 110 cm,

110 = 14x / 4

4 x 110 = 14x

440 = 14x

x = 440/14 = 31.42 cm

Breadth = 3/4 of x = 23.55

Length = x = 31.42