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In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y.

In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Rectilinear Figures

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Answer

In parallelogram opposite sides are equal.

∴ BC = AD = 2x and

AB = CD

⇒ 3x = 2y + 2

⇒ 2y = 3x - 2

⇒ y = 3x22\dfrac{3x - 2}{2} ……..(i)

Given, perimeter = 40.

⇒ AB + BC + CD + AD = 40

⇒ 3x + 2x + 2y + 2 + 2x = 40

⇒ 3x + 2x + 2(3x22)2\Big(\dfrac{3x - 2}{2}\Big) + 2 + 2x = 40

⇒ 3x + 2x + 3x - 2 + 2 + 2x = 40

⇒ 10x = 40

⇒ x = 4.

⇒ y = 3x22=3×422=1222=5\dfrac{3x - 2}{2} = \dfrac{3 \times 4 - 2}{2} = \dfrac{12 - 2}{2} = 5.

Hence, x = 4 and y = 5.

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