Mathematics
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
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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 =
⇒ 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 = = 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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