Question

The perimeter of parallelogram ABCD is 42cm. If AP=3Cm, and AQ=4Cm, Calculate the sides of parallelogram ABCD. PLEASE answer it ​

Answer 1

Given :-

• Perimeter of parallelogram ABCD = 42cm.
• AP = 3cm.
• AQ = 4cm.

To Find :-

• Sides of Parallelogram ?

Formula used :-

• Opposite Sides of parallelogram are Equal in Length.
• Perimeter of Parallelogram = 2(Length + Breadth)
• Area of Parallelogram = Base * Corresponding Height on Base.

Solution :-

Let us Assume That, Length & Breadth of Parallelogram are L & B.

So,

→ AD = BC = L

→ AB = DC = B

So,

→ Perimeter of Parallelogram = 2(L + B)

→ 2(L + B) = 42

→ L + B = 21

→ L = (21 - B) --------------- Equation (1)

_____________________

Now,

→ Base DC = B

→ Length of Perpendicular on DC = AQ = 4cm.

So,

→ Area of Parallelogram = Base * Perpendicular = (B * 4) --------------- Equation (2)

Similarly,

→ Base BC = L

→ Length of Perpendicular on BC = AP = 3cm.

So,

→ Area of Parallelogram = Base * Perpendicular = (L * 3) --------------- Equation (3)

_____________________

Now,

→ Area of Parallelogram = Equation (2) = Equation (3)

→ Equation (2) = Equation (3)

→ 4B = 3L

Putting value of Equation (1) Now,

→ 4B = 3(21 - B)

→ 4B = 63 - 3B

→ 4B + 3B = 63

→ 7B = 63

→ B = 9 cm. (Ans.)

Putting This value in Equation (1) ,

→ L = 21 - B

→ L = 21 - 9

→ L = 12 cm. (Ans.)

Hence, Sides AB , BC, CD , DA of Parallelogram are 9, 12, 9 & 12cm Respectively.

Answer 2

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QUESTION :

The perimeter of parallelogram ABCD is 42cm. If AP=3Cm, and AQ=4Cm, Calculate the sides of parallelogram ABCD. PLEASE answer it .

SOLUTION :

See the attachment in the figure.

The following information is given :

Perimeter = 42 cm.

AP = 3 cm.

AQ = 4 cm.

Calculate the sides of parallelogram ABCD..

In a Parallelogram, opposite sides are equal in length.

Let AD = BC = X

Let AB = CD = Y

Perimeter = 2 ( X + Y )

We know that the area it's a Parallelogram is equal to The product of the base and it's Corresponding Height..

=> Area of Parallelogram = AD × AP = AB × AQ

=> X × AP = Y × AQ

AP = 3 cm.

AP = 3 cm.AQ = 4 cm.

So,

3 X = 4 Y .......... [ 1 ]

2 X + 2 Y = 42 ............ [ 2 ]

Y = 3 / 4 X

=> 2 X + 3 / 2 X = 42

=> 7 X = 84

=> X = 12 m.

2 × 12 + 2 Y = 42

=> Y = 9 m.

So the sides of the Parallelogram are 12 m, 9 m, 12 m and 9 m respectively.

ANSWER :

The sides of the Parallelogram are 12 m, 9 m, 12 m and 9 m respectively.