A trapezium with parallel sides of length as 7:3 is cut from a rectangle 30 DM by 4 DM so as to have an area of one-third the latter. find the lengths of the parallel sides.
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A trapezium with parallel sides of length as 7:3 is cut from a rectangle 30 DM by 4 DM so as to have an area of one-third the latter. find the lengths of the parallel sides.
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Step-by-step explanation:
Given Length of the Rectangle = ab=40 dm and breadth of the rectangle = bc = 3 dm
therefore area of the rectangle = 40\times3=12040×3=120 dm²
The area of the trapezium = 1/3 of the area of the rectangle = 40 dm²
Consider the length of the parallel side of the trapezium are 7x and 3x
we know that the area of trapezium = h\times(\frac{a+b}{2})h×(
2
a+b
)
where h = height of the trapezium
a and b are the two side.
therefore
\begin{gathered}40=3\times(\frac{7x+3x}{2})\\\\40=3\times(\frac{10x}{2})\\\\40=3\times5x\\\\40=15x\\\\x=\frac{40}{15}\end{gathered}
40=3×(
2
7x+3x
)
40=3×(
2
10x
)
40=3×5x
40=15x
x=
15
40
Puting the value of x we get the length of the two side are
a=7\times\frac{40}{15}=18.6 dma=7×
15
40
=18.6dm and b=3\times\frac{40}{15}= 8 dmb=3×
15
40
=8dm
Answer:
a=18.6 dm and b= 8 dm
Step-by-step explanation:
Given Length of the Rectangle = ab=40 dm and breadth of the rectangle = bc = 3 dm
therefore area of the rectangle = dm²
The area of the trapezium = 1/3 of the area of the rectangle = 40 dm²
Consider the length of the parallel side of the trapezium are 7x and 3x
we know that the area of trapezium =
where h = height of the trapezium
a and b are the two side.
therefore
Puting the value of x we get the length of the two side are
and