Question

The area of trapezium is 432 m '2 the perpendicular diatnce between the two paralle side is 18m .iof the the difference of the parallel sides is 18m find the lengths of the parallel sides

Answer 1

AnswEr:-

Lengths of parallel sides = 33 m & 15 m

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Given:-

• Area of trapezium = 432 m²
• Perpendicular distance = 18 m
• Difference between parallel sides = 18 m

To find:-

• Parallel sides = ?

Solution:-

Let the parallel sides be m & n m respectively.

↠ m - n = 18

↠ m = n + 18 -(Eq.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

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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.

Answer 2

Given,

• Area of Trapezium = 432m²
• Height = 18 m

To Find ,

• The length of the parallel sides = ?

Solution :

Let the parallel side length be x and y

We Know that :

$\implies \boxed{\bold{Area \ of \ Trapezium = \frac{1}{2} \times Height \times (Sum \ of \ parallel \ sides)}}$

$\implies \bold{432 = \frac{1}{2} \times 18 \times (x + y)}$

$\implies \bold{\frac{432}{9} = x + y}$

$\implies \bold{48 = x + y}$

$\implies \bold{x = 48 - y}$............1) Equation

Now Given in this question that the difference between two parallel side is 18 :

∴ $\implies \bold{ x - y = 18}$.......2) Equation

$\implies \bold{48 - y - y = 18}$.......{From Equation 1)}

$\implies \bold{48 - 2y = 18}$

$\implies \bold{-2y = 18 - 48}$

$\implies \bold{-2y = -30}$

$\implies \boxed{\bold{ y = 15 m}}$

Now put value of y in 2 Equation :

∴$\implies \bold{x = 48 - 15}$

$\implies \boxed{\bold{x = 33 m}}$

∴First parallel side = 33 m

Second Parallel side = 15 m

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