Question

ABCD is a parallelogram with perimeter 40b. find the values of x and y​

Answer 1

Given :

• ABCD is a parallelogram with perimeter =40cm

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To Find :

• The value of x and y=?

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Formula :

• Perimeter of parallelogram =2(L+b)

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Solution:

$\\ \pink{\bf{Sides}} \begin{cases} \: \sf{Length(DC)=2y+2} \\ \\ \sf{Breadth(DA)=2x} \\ \\\sf{AB=3x} \end{cases}$

$\\ \\ \implies \sf \: perimeter \: of \: parallelogram = 2(l + b) \\ \\ \\ \implies \sf \: perimeter \: of \: parallelogram = 40cm \\ \\ \\ \implies \sf \: 40 = 2(l + b) \\ \\ \\ \implies \sf \: \frac{40}{2} = (2y + 2) + 2x \\ \\ \\ \implies \sf \: 20 = 2y + 2x + 2 \\ \\ \\ \implies \sf \: 18 = 2x + 2y \\ \\ \\ \implies \sf \: 9 = x + y \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \boxed{ \sf{9 - y = x}} \: \: \: \: \: \: \: \: \: \: .....(1)$

Also, Opposite sides of parallelogram are equal .

$\therefore \: \: \: \: \: \implies \sf \: 3x = 2y + 2 \\ \\ \\ \implies \sf \: 3x - 2y - 2 = 0 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \boxed{ \sf{3x - 2y = 2}} \: \: \: \: \: \: \: \: \: \: \: \: \: ........(2)$

On putting equations (1) in equation (2) we get,

$\\ \implies \sf \: 3( 9 - y) - 2y = 2 \\ \\ \implies \sf \: 27 - 3y - 2y = 2 \\ \\ \implies \sf \: 27 - 5y -2 = 0 \\ \\ \implies \sf \: 25 - 5y = 0 \\ \\ \implies \boxed{ \sf{y = 5}}$

Putting the value of y in equation (1) we get,

$\implies \sf \: x = 9 - 5 \\ \\ \implies \boxed{ \sf{x = 4}}$

Hence, the value of X and y are

$\green \bigstar\boxed{ \bf{x = 4}} \: \: \: \tt{and }\: \: \boxed{ \bf{y = 5}}$