Question

8. The area of trapezium is 640 cm². If its parallel sides are in the ratio 2 : 3 and the perpendicular distance between the two is 16 cm, find length of each parallel side.​

Answer 1

$\frak{Given}\begin{cases}\sf{\quad Area \: of \: trapezium = \bf{640\;cm^2}}\\\sf{\quad Side_{ \: 1} : Side_{ \: 2} = \bf{2:3}} \\\sf{\quad Distance \: b/w \: them = \bf{16 \;cm}}\end{cases}$

$\frak{To\;find:}$ Length of each // side?

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❍ Let's say, that the // side of the given trapezium be 2x and 3x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

$\qquad\:\star\;\underline{\boxed{\pmb{\frak{Area_{\;(trapezium)} = \dfrac{1}{2}\bigg \lgroup x + y\bigg\rgroup h}}}}$

where:

• x and y are the // sides of trapezium.
• h is the distance b/w the // sides.
• Given area is 640 cm².

⠀⠀

⠀⠀$\underline{\bf{\dag} \:\mathfrak{Substituting\;values\;in\; formula\: :}}$

$:\implies\sf 640 = \dfrac{1}{2}\bigg\lgroup 3x + 2x \bigg\rgroup 16 \\\\\\:\implies\sf 640 = \dfrac{ \: 1}{\cancel{\;2}} \times 5x \times \: \cancel{16}\\\\\\:\implies\sf 640 = 5x \times 8\\\\\\:\implies\sf 640 = 40x\\\\\\:\implies\sf x = \cancel\dfrac{640}{40}\\\\\\:\implies\underline{\boxed{\pmb{\frak{\red{x = 16}}}}}\;\bigstar$

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Therefore,

• Length of // Side₁ = 2x = 2(16) = 32 cm
• Length of // Side₂ = 3x = 3(16) = 48 cm

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$\therefore{\underline{\textsf{Hence, the length of the parallel sides are \textbf{32 cm, 48 cm} respectively.}}}$

Answer 2

Answer:

Given :-

• The area of trapezium is 640 cm².
• The parallel sides are in the ratio of 2 : 3 and the perpendicular distance between the two sides is 16 cm.

To Find :-

• What are the length of each parallel sides.

Formula Used :-

$\clubsuit$ Area Of Trapezium Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Trapezium)} =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides \times Height}}}$

Solution :-

Let,

$\leadsto \bf{Length\: of\: first\: side_{(Trapezium)} =\: 2y\: cm}$

$\leadsto \bf{Length\: of\: second\: side_{(Trapezium)} =\: 3y\: cm}$

According to the question by using the formula we get,

$\implies \sf \dfrac{1}{2} \times \bigg(2y + 3y\bigg) \times 16 =\: 640$

$\implies \sf \dfrac{1}{2} \times 5y \times 16 =\: 640$

$\implies \sf 5y \times 16 =\: 640 \times 2$

$\implies \sf 5y \times 16 =\: 1280$

$\implies \sf 5y =\: \dfrac{\cancel{1280}}{\cancel{16}}$

$\implies \sf 5y =\: 80$

$\implies \sf y =\: \dfrac{\cancel{80}}{\cancel{5}}$

$\implies \sf \bold{\purple{y =\: 16\: cm}}$

Hence, the required length of parallel sides are :

❒ Length of first side of trapezium :

$\longrightarrow \sf Length\: of\: first\: side_{(Trapezium)} =\: 2y\: cm$

$\longrightarrow \sf Length\: of\: first\: side_{(Trapezium)} =\: 2 \times 16\: cm$

$\longrightarrow \sf\bold{\red{Length\: of\: first\: side_{(Trapezium)} =\: 32\: cm}}$

❒ Length of second side of trapezium :

$\longrightarrow \sf Length\: of\: second\: side_{(Trapezium)} =\: 3y\: cm$

$\longrightarrow \sf Length\: of\: second\: side_{(Trapezium)} =\: 3 \times 16\: cm$

$\longrightarrow \sf\bold{\red{Length\: of\: second\: side_{(Trapezium)} =\: 48\: cm}}$

${\small{\bold{\underline{\therefore\: The\: length\: of\: each\: parallel\: sides\: are\: 32\: cm\: and\: 48\: cm\: respectively\: .}}}}$