From a rectangular sheet 31 cm long and 22 cm wide, a trapezium-shaped piece is cut out. The area of the remaining sheet is 298 cm². One of the parallel sides of the trapezium-shaped piece is 3/5th of the other and the parallel sides are 12cm apart. Find the length of each parallel side.
Answers
Length of parallel sides is 24 cm and 40 cm
Given:
i) A rectangular sheet 31 cm long and 22 cm wide
ii) A trapezium-shaped piece is cut out from this rectangular sheet, whose one of the parallel sides is 3/5th of the other and the parallel sides are 12 cm apart
iii) The area of the remaining sheet is 298 cm²
To find:
The length of each parallel side.
Solution:
Area of rectangular sheet = lb
= 31*22
= 682 cm²
Area of the remaining sheet = 298 cm²
Therefore,
Area of the trapezium-shaped piece = 682 - 298
= 384 cm²
Let one of the parallel sides of the trapezium-shaped piece be x, then the other side = (3/5)x
Height of the trapezium-shaped piece = h = 12 cm
Area of the trapezium-shaped piece
= (1/2)(Sum of the parallel sides)(height)
= (1/2)(x + (3/5)x)(12)
= (1/2)((8/5)x)(12)
= 48x/5 = 384
=> 48x/5 = 384
=> x = 384*5/48
=> x = 40 cm
Therefore, the other side = (3/5)x
= (3/5)40
= 24 cm
Hence,
length of each parallel side is 24 cm and 40 cm
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