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 (Fig. 9.42).
Solution:
Given, the perimeter of a parallelogram shaped land is 96 m
The area of parallelogram shaped land is 270 m².
One of the sides of the parallelogram is 18 m
We have to find the length of the other side.
Consider a parallelogram ABCD,
AB = CD = 18 m
BC = AD
Perimeter of parallelogram ABCD = AB + BC + CD + AD
96 = 18 + AD + 18 + AD
96 = 36 + 2 AD
2AD = 96 - 36
2AD = 60
AD = 60/2
AD = 30 m
So, BC = AD = 30 m
Therefore, the length of the other side is 30 m.
We have to find the lengths of altitudes l and m.
Area of parallelogram = base × corresponding height
Area of parallelogram ABCD = AB × DE
270 = 18 × DE
DE = 270/18
DE = 15 m
Similarly, 270 = AD × BF
270 = 30 × BF
BF = 270/30
BF = 9 m
Here, DE = m = 15 m
BF = l = 9 m
Therefore, the lengths of altitudes l and m are 9 m and 15 m.
✦ Try This: Perimeter of a parallelogram shaped land is 90 m and its area is 320 square metres. If one of the sides of this parallelogram is 20 m, find the length of the other side. Also, find the lengths of altitudes l and m.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 89
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 (Fig. 9.42).
Summary:
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, the length of the other side is 30 m. Also, the lengths of altitudes l and m are 9 m and 15 m
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