in the figure,. ABCD is a ||gm in which DC||AB, AD||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 ||gm.
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AB = 3x - 5, BC = 2y - 7, CD = x + 7, AD = y + 3.
In the question, It is given parallelogram.
In the parallelogram, Opposite sides are parallel and equal.
1.
AB = CD.
=> 3x - 5 = x + 7
=> 3x - x = 7 + 5
=> x = 6
(a)
Hence the value of x = 6.
(b)
AB = 3x - 5
=> 3(6) - 5
=> 13 cm
(c)
BC = AD
=> 2y - 7 = y + 3
=> 2y - y = 10
=> y = 10
(d)
AD = y + 3 = 13 cm
(e)
Perimeter = AB + BC + CD + DA
=> 13 + 13 + 13 + 13
=> 52 cm
Answers for Questions:
1.
I have solved using parallelogram properties. Opposite sides are parallel and equal
2.
To determine lengths of AB and AD, Apply the parallelogram properties.
#Hope my answer helped you
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