Question

$\huge\underline\bold\blue{Question}$

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

Step-by-step explanation:

Parallel sides = 2x and 3x (common factor is assumed as x)

Area = 420

Perpendicular distance = 8

Now put the value in formula.

420 = [(2x + 3x)/2] * 8

5x = 420/4

x = 105/5

x = 21

Hence, parallel sides of trapezium is 42 (2*21) and 63 (3*21).

Answer 2

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

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

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❍ Let's Consider that, the // sides of the trapezium are 2x and 3x respectively.

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

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$\qquad\star\;\underline{\boxed{\frak{\pmb{Area\;_{(trapezium)}=\dfrac{1}{2}\bigg\lgroup a+b\bigg\rgroup h}}}}$

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where,

• a & b are the two // sides of the trapezium.
• h is the height or distance b/w the // sides.
• Area of the trapezium is 640 cm².

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$\quad\underline{\bf{\dag}\frak{\;Substituting\;the\;values\;in\;the\;formula\;:}}$

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

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

Therefore,

• Length of side 1 = 2x = 2(16) = 32 cm
• Length of side 2 = 3x = 3(16) = 48 cm

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$\therefore\;{\underline{\textsf{Hence,\;the\;sides\;of\:the\;trapezium\;are\;{\textbf{32\;cm}}\;\&\;{\textbf{48\;cm}}}.}}$⠀⠀⠀