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Question
Perimeter of a parallelogram shaped land is 96 m and its area is 270 square metres. If one of the sides of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m (see figure).
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Solution
Given, perimeter of parallelogram = 96 m and area of parallelogram = 270 m2
In a parallelogram ABCD, AB = CD = 18 m and AD = BC
As we know, perimeter of a parallelogram ABCD = AB + BC + CD + AD
⇒ 96 = 18 + AD + 18 + AD ...[∵ AD = BC]
⇒ 96 = 36 + 24D
⇒ 2AD = 60
⇒ AD = 30 cm
So, AD = BC = 30 cm
Now, area of parallelogram ABCD = Base × Corresponding height
⇒ 270 = AB × DE ...[∵ Base = AB]
⇒ 270 = 18 × DE
⇒ `270/18` = DE
⇒ DE = 15 m
Also, area of parallelogram ABCD = AD × BF ...[∵ Base = AD]
⇒ 270 = 30 × l
⇒ l = `270/30`
⇒ l = 9 m
Hence, altitudes l = 9 m and m = 15 m.
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