Question

The perimeter of a parallelogram is 200 cm. One of its side is greater than the other by 50 cm. Find length of all sides of the parallelogram

Answer 1

the sides are 75cm and 25 cm

Answer 2

Given

Perimeter of Parallelogram ⇒ 2(a + b)

Perimeter of Parallelogram ⇒ 200 cm

One side of the Parallelogram ⇒ x + 50

Another side of the Parallelogram ⇒ x

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To Find

All the sides of the parallelogram

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Solution

Let's consider one side of the parallelogram to be 'x'

Perimeter of Parallelogram ⇒ 2(a + b)

Perimeter of Parallelogram ⇒ 200 cm

One side of the Parallelogram ⇒ x + 50

Another side of the Parallelogram ⇒ x

We know that the opposite of the parallelogram are equal, hence the perimeter of the parallelogram would be equal to the sum of all the sides.

We'll solve this equation to find the value of 'x' ⇒ $x+(x+50)+x+(x+50)=200$

Let's solve this equation step-by-step.

$x+(x+50)+x+(x+50)=200$

Step 1: Simplify both sides of the equation.

$x+x+50+x+x+50=200$

(Combine Like Terms)

$(x+x+x+x)+(50+50)=200$

$4x+100=200$

Step 2: Subtract 100 from both sides.

$4x+100-100=200-100$

$4x=100$

Step 3: Divide both sides by 4.

$\dfrac{4x}{4} =\dfrac{100}{4}$

$x=25$

Since we know the value of 'x' we will substitute the values now.

Side 1 = x = 25 cm

Side 2 = x+50 = 25+50 = 75 cm

Side 3 = x = 25 cm

Side 4 = x+50 = 25+50 = 75 cm

∴ The lengths of the parallelogram are ⇒ 25 cm, 75 cm, 25 cm, 75 cm.

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