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प्रश्न
The perimeter of a parallelogram ABCD is 48 cm. If BC = 3x – 2, DA = x + 2y + 2 and AB = 3y + 2, find the values of x and y.
बेरीज
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उत्तर
Given: Parallelogram ABCD with perimeter 48 cm.
BC = 3x – 2
DA = x + 2y + 2
AB = 3y + 2
Step-wise calculation:
1. In a parallelogram, opposite sides are equal.
So, BC = DA.
Hence, 3x – 2 = x + 2y + 2.
Simplify:
3x – x = 2y + 2 + 2
⇒ 2x = 2y + 4
⇒ x = y + 2 ...(Equation 1)
2. Perimeter = 2(AB + BC) = 48
⇒ AB + BC = 24
Substitute AB and BC:
(3y + 2) + (3x − 2) = 24
⇒ 3x + 3y = 24
⇒ x + y = 8 ...(Equation 2)
3. Substitute equation 1 into equation 2:
(y + 2) + y = 8
⇒ 2y + 2 = 8
⇒ 2y = 6
⇒ y = 3
4. Then x = y + 2
= 3 + 2
= 5
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