Question

the area of a trapezium is 420 m^2 . the perpendicular distance between the two parallel sides is 21 m . if the difference of the parallel sides is 18 m , find the lengths of the parallel sides.

Answer 1

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Answer 2

Aɴꜱᴡᴇʀ

$\large\sf{\fbox{\fbox{\orange{Lengths \:of \:parallel\: sides \:= 33\: m \:and\: 15 \:m}}}}$

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Gɪᴠᴇɴ

Area of trapezium = 432 m²

Perpendicular distance = 18 m

Difference between parallel sides = 18 m

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ᴛᴏ ꜰɪɴᴅ ᴛᴏ ᴘʀᴏᴠᴇ

Parallel sides = ?

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Sᴛᴇᴘꜱ

Let the parallel sides be m & n m respectively.

↠ m - n = 18

↠ m = n + 18 ---------------1

We know,

☛ Area of trapezium = ½ (Sum of sides) × Perpendicular distance

Putting values:-

⇒ 432 = ½ (m + n) × 18

⇒ 432 = ½ (n + 18 + n) × 18

[∵ From Eq.1 : m = n + 18 ]

⇒ 432 = ½ (2n + 18) × 18

⇒ 432 = 9 (2n + 18)

⇒ 2n + 18 = 432/9

⇒ 2(n + 9) = 48

⇒ n + 9 = 48/2

⇒ n + 9 = 24

⇒ n = 24 - 9

⇒ n = 15

∴ One parallel side = 15 m

Putting this value in (Eq.1)

⇒ m = 15 + 18

⇒ m = 33

∴ Another parallel side = 33 m

Therefore,

Lengths of Parallel sides of trapezium are 33 m & 15 m respectively.

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$