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In figure (1) given below, the perimeter of the parallelogram is 42 cm. Calculate the lengths of the sides of the parallelogram.

In figure (1) given below, the perimeter of the parallelogram is 42 cm. Calculate the lengths of the sides of the parallelogram. Theorems on Area, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Theorems on Area

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Answer

Let AB = p

Since, opposite sides of || gm are equal.

Perimeter of || gm ABCD = 2(AB + BC)

⇒ 42 = 2(p + BC)

⇒ p + BC = 422\dfrac{42}{2}

⇒ p + BC = 21

⇒ BC = 21 – P

area of ||gm ABCD = base × height = AB × DM = p × 6 = 6p …….(i)

Also, area of ||gm ABCD = BC × DN

= (21 – p) × 8

= 8(21 – p) ………… (ii)

From (i) and (ii), we get

⇒ 6p = 8(21 – p)

⇒ 6p = 168 – 8p

⇒ 6p + 8p = 168

⇒ 14p = 168

⇒ p = 16814\dfrac{168}{14} = 12 cm.

⇒ 21 - p = 21 - 12 = 9 cm.

Hence, the sides of ||gm are AB = 12 cm and BC = 9 cm.

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