Question

1. In the figure, ABCD is a parallelogram in which
DC UAB, AD II BC, and DC = (3x - 1) cm, CB=5(y -1) cm,
BA = (x + 7) cm and AD = (2y +1) cm.
Find x, y, and the perimeter of the parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

Answer:-

Given:-

• The given figure as a Parallelogram
• We need to find the x and y in the given figure.

Attachment :-

The properties of parallelogram are attached in the attachment. With the help of the attachment we can solve it.

Let's Solve!

$\sf{(3x-1) = (x+7)}$

$\sf{3x-x= 7+1}$

$\sf{2x= 8}$

$\sf{x = 4}$ is the first answer.

$\rm{2y+1 = 5y-5}$

$\rm{2y-5y = -5-1}$

$\rm{-3y = -6}$

$\rm{y = 2}$ is the required 2nd answer.

So, the value of x is 4 and value of y is 2.

Finding Perimeter:-

2y+1 = 2(2)+1 = 4+1 = 5 cm

x+7 = 4+7 = 11 cm

5(y-1) = 5(2-1) = 5*1 = 5 cm

3x-1 = 3(4)-1 = 11 cm

So, Perimeter = 2(11+5) = 2(16) = 32 cm

Answer 2

${\large{\bold{\rm{\underline{Correct \; question}}}}}$

★ In the figure, ABCD is a parallelogram in which DC||AB and AD||BC and DC measure (3x-1) cm, BC measure 5(y-1) cm, AD measures (2y+1) cm and AB measures (x+7) cm. Find the value of x and y and the perimeter of parallelogram too.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ DC is parallel to AB

★ AD is parallel to BC

★ DC measure (3x-1) cm

★ BC measure 5(y-1) cm

★ AD measures (2y+1) cm

★ AB measures (x+7) cm

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Value of x

★ Value of y

★ Perimeter of parallelogram

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Value of x = 4

★ Value of y = 2

★ Perimeter of parallelogram = 32 cm

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

~ According to the question as it's given in the parallelogram sides, DC||AB and AD||BC means DC is parallel to AB and AD is parallel to BC. It is already cleared that these sides are equal to each other...!

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

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~ Firstly, let's find the value of x (by using property that parallel sides are equal)..!

${\tt{:\implies (3x-1) \: = \: (x+7)}}$

${\tt{:\implies 3x-1 \: = \: x+7}}$

${\tt{:\implies 3x - \: x = \: 7 \: + 1}}$

${\tt{:\implies 3x - \: 1x = \: 7 \: + 1}}$

${\tt{:\implies 2x = \: 8}}$

${\tt{:\implies x \: = 8/2}}$

${\tt{:\implies x \: = 4}}$

${\small{\boxed{\bf{Henceforth, \: value \: of \: x \: is \: 4}}}}$

_______________________

~ Now let's find the value of y (by using property that parallel sides are equal)..!

${\tt{:\implies (2y+1) \: = \: 5(y-1)}}$

${\tt{:\implies 2y+1 \: = \: 5y-5}}$

${\tt{:\implies 2y \: - 5y \: = -5 -1}}$

${\tt{:\implies -3y \: = -6}}$

${\tt{:\implies 3y \: = 6}}$

${\tt{:\implies y \: = 6/3}}$

${\tt{:\implies y \: = 2}}$

${\small{\boxed{\bf{Henceforth, \: value \: of \: y \: is \: 2}}}}$

_______________________

~ Now let's find the perimeter of this parallelogram..!

Firstly, let us find for y then for x then using formula to find the perimeter of parallelogram...!

We have to imply the value of y and x as 2 and 4 respectively too..!

For (2y+1)

${\tt{:\implies (2y+1)}}$

${\tt{:\implies 2y+1}}$

${\tt{:\implies 2(2)+1}}$

${\tt{:\implies 2 \times 2 +1}}$

${\tt{:\implies 4 +1}}$

${\tt{:\implies 5 \: cm}}$

For 5(y-1)

${\tt{:\implies 5(y-1)}}$

${\tt{:\implies 5(2-1)}}$

${\tt{:\implies 10 - 5}}$

${\tt{:\implies 5 \: cm}}$

For (x+7)

${\tt{:\implies (x+7)}}$

${\tt{:\implies x+7}}$

${\tt{:\implies 4+7}}$

${\tt{:\implies 11 \: cm}}$

For (3x-1)

${\tt{:\implies (3x-1)}}$

${\tt{:\implies 3x-1}}$

${\tt{:\implies 3(4) -1}}$

${\tt{:\implies 3 \times 4 -1}}$

${\tt{:\implies 12 -1}}$

${\tt{:\implies 11 \: cm}}$

_______________________

~ Now at last let's find the perimeter of the parallelogram..!

${\tt{:\implies 2(Sum \: of \: parallel \: sides)}}$

${\tt{:\implies 2(11 + 5)}}$

${\tt{:\implies 2(16)}}$

${\tt{:\implies 2 \times 16}}$

${\tt{:\implies 32 \: cm}}$

${\small{\boxed{\bf{Henceforth, \: perimeter \: is \: 32 \: cm}}}}$

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