All parallelograms having equal areas have the same perimeters. Is the given statement true or false?
Solution:
Given, all parallelograms having equal areas have the same perimeters.
We have to determine if the given statement is true or false.
Area of parallelogram = base × corresponding height
= b × h square units
Perimeter of parallelogram = 2(length + breadth)
= 2(a + b) units
The corresponding height and side of two parallelograms can be different.
Therefore, all parallelograms with equal areas need not have the same perimeters.
✦ Try This: The perimeter of square is 36 cm. Find the length of its diagonal.
Given, the perimeter of the square is 36 cm.
We have to find the length of its diagonal.
Perimeter = 4(side)
36 = 4(side)
Side = 36/4
= 9 cm
Area of square = (side)²
= (9)²
= 81 cm²
Area of square = 1/2 × (diagonal)²
81 = 1/2 × (diagonal)²
(diagonal)² = 81(2)
(diagonal)² = 162
Taking square root,
Diagonal = 9√2
= 9(1.414)
= 12.73 cm
Therefore, the diagonal of the square is 12.73 cm.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 61
All parallelograms having equal areas have the same perimeters. Is the given statement true or false?
Summary:
The given statement, “All parallelograms having equal areas have the same perimeters” is false.
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