Question

7. The difference of the parallel sides of a trapezoidal field is 20 m. Its area is 450 m² and its altitude is 15 m.​ Find the length of the parallel sides.​

Answer 1

Required Answer :

Given:

• The difference of the parallel sides of a trapezoidal field is 20 m.

• Area = 450 m²

• Altitude = 15 m

To calculate:

• Length of parallel sides.

Calculation:

Let the length of the parallel sides be x and y respectively.

• x is longer side.
• y is smaller side.

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★ According to the question :

$\sf {\dashrightarrow x - y = 20 }$

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$\sf {\dashrightarrow x = 20 + y . . . . . . . (i) }$

As we know that,

$\underline{\boxed {\sf { \star {Area}_{(Trapezium)} = \dfrac{1}{2} \times h \times (sum \: of \: parallel \: sides)} }}$

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$\sf { \dashrightarrow 450 = \dfrac{1}{2} \times 15 \times (sum \: of \: parallel \: sides)}$

• Sum of parallel sides = x + y
• Sum of parallel sides = (20+y)+y

⠀⠀» Substituting value of x from eq. (i)

Now,

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$\sf { \dashrightarrow 450 = \dfrac{1}{2} \times 15 ( 20 +2y) }$

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$\sf { \dashrightarrow 450 = \dfrac{1}{2} \times 300 + 30y }$

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$\sf { \dashrightarrow 450 \times 2 = 300 + 30y }$

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$\sf { \dashrightarrow 900 = 300 + 30y }$

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$\sf { \dashrightarrow 900 -300 = 30y }$

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$\sf { \dashrightarrow 600 = 30y }$

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$\sf { \dashrightarrow \dfrac{600}{30} = y }$

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$\sf { \dashrightarrow 20 = y }$

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$\boxed {\bf { \dashrightarrow 20 \: m = Smaller \: side}}$

$\underline{\sf{\therefore \: Length \: of \: y (smaller \: side) \: is 20 \: m }}$

Also,

$\sf { \dashrightarrow x -y = 20}$

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$\sf { \dashrightarrow x -20 = 20}$

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$\sf { \dashrightarrow x = 20+20}$

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$\sf { \dashrightarrow x = 40}$

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$\boxed {\bf { \dashrightarrow 40 \: m = Longer \: side}}$

$\underline{\sf{\therefore \: Length \: of \: x (longer \: side) \: is 40 \: m }}$