Question

the area of a trapezium is 0.05m² and its height is 20 CM. If one of the parallel side is shorter than the other by 8 CM, find the length of the longer side ​

Answer 1

The area of a trapezium is 0.05 m²·

Height (h) of trapezium is 20 cm or 0.2 m.

One of the parallel side is shorter than the other by 8 cm.

Let,

a be the one of the parallel side which is longer than other.

And b be the shorter side.

\begin{gathered}\begin{gathered}\bf\purple{According\:to\:the\:question,} \\ \end{gathered} \\ \begin{gathered}\longmapsto\:\:\bf\green{b\:=\:(a\:-\:8)} \\ \end{gathered} \\ \begin{gathered}\bf\blue{We\:know\:that,} \\ \end{gathered} \\ \begin{gathered}\red\bigstar\:\:\bf{\color{peru}Area\:=\:\dfrac{1}{2}\:h\:(a\:+\:b)\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{0.05\:=\:\dfrac{1}{2}\times{0.2}\:(a\:+\:a\:-\:8)\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{0.05\:=\:0.1\:(2a\:-\:8)\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{2a\:-\:8\:=\:\dfrac{0.05}{0.1}\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{2a\:=\:0.5\:+\:8\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{2a\:=\:8.5\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf{a\:=\:\dfrac{8.5}{2}\:} \\ \end{gathered} \\ \begin{gathered}:\implies\:\:\bf\orange{a\:=\:4.25\:m\:} \\ \end{gathered} \\\end{gathered}

Accordingtothequestion,

⟼b=(a−8)

Weknowthat,

★Area=

2

1

h(a+b)

:⟹0.05=

2

1

×0.2(a+a−8)

:⟹0.05=0.1(2a−8)

:⟹2a−8=

0.1

0.05

:⟹2a=0.5+8

:⟹2a=8.5

:⟹a=

2

8.5

:⟹a=4.25m

Answer 2

the area of a trapezium is 0.05m² and its height is 20 CM. If one of the parallel side is shorter than the other by 8 CM, find the length of the longer side

One of the parallel side of trapezium is shorter than the other by 8 cm.

⠀⠀⠀⠀

Now,

☯ Let one side of trapezium be x cm.

Therefore, Other side will be (x + 8) cm.⠀⠀⠀⠀Therefore,

One parallel side of trapezium, x = 21 cm

Other parallel side of trapezium, (x + 8) = 29 cm

⠀⠀⠀⠀

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