Question
Download Solution PDFThe two adjacent sides of a parallelogram are 12 cm and 5 cm respectively. If one of the diagonals is 13 cm long, then what is the area of the parallelogram?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven Data:
Two adjacent sides: 12 cm and 5 cm
One diagonal: 13 cm
Concept Used:
Area of a parallelogram: Area = base × height.
Every rectangle is a parallelogram.
Calculation:
Use Pythagoras in the triangle formed by sides and diagonal:
122 + 52 = 132
Since these sides are Triples, so it form the right angle triangle.
So length = 12 and height = 5
So, this is only possible in a rectangle, as every rectangle is a parallelogram, not every parallelogram is a rectangle.
⇒ Area of parallelogram: 12 × 5 = 60 cm2
Therefore, the area of the parallelogram is 60 cm2.
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