Question

The length and breadth of a rectangular park is 50m and 30m respectively. Find the length of the diagonal correct upto two decimal places
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Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• The length of a rectangular park is 50m

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• The Breadth of a rectangular park is 30m

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• The length of its diagonal

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the diagonal be "d"

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As a diagonal of a rectangle divides the rectangle into 2 right angled triangle having base and height equal to length or breadth.

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Thus , by Pythagoras theorem

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➠ Hypotenuse² = Base² + Length²

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Here ,

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• Hypotenuse = Diagonal = d

• Base = Breadth = 30 m

• Height = Length = 50 m

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So,

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➜ d² = 30² + 50²

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➜ d² = 900 + 2500

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➜ d² = 3400

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➜ $\sf d = \sqrt { 3400 }$

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➨ d ≈ 58.50 m

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• Hence the length of diagonal is 58.50 m

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Additional information

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Perimeter of rectangle

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• 2(Length + Breadth)

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Area of rectangle

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• Length × Breadth

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Properties of rectangle

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• A rectangle is a quadrilateral.

• The opposite sides are parallel and equal to each other.

• Each interior angle is equal to 90 degrees.

• The sum of all the interior angles is equal to 360 degrees.

• The diagonals bisect each other.

• Both the diagonals have the same length.

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Answer 2

Answer :

›»› The length of the diagonal 58.30 m.

Given :

• The length and breadth of a rectangular park is 50m and 30m respectively.

To Find :

• The length of the diagonal correct upto two decimal places.

Solution :

Let us assume that, the length of the diagonal is "x m".

To find the length of the diagonal of, by using Pythagoras theorem :-

❰ Hypotenuse² = Perpendicular ² + Base² ❱

• Hypotenuse = Diagonal = ?
• Perpendicular = Length = 50 m.
• Base = Breadth = 30 m.

According to the given question,

On putting the given values in the formula, we get

→ Diagonal² = Length² + Breadth²

→ x² = (50)² + (30)²

→ x² = 2500 + 900

→ x² = 3400

→ x = √3400

→ x = 58.30

Hence, the length of the diagonal 58.30 m.

Verification :

→ Hypotenuse² = Perpendicular ² + Base²

→ Diagonal² = Length² + Breadth²

→ 58.30² = (50)² + (30)²

→ 58.30² = 2500 + 900

→ 58.30² = 3400

→ 58.30 = √3400

→ 58.30 = 58.30

Clearly, LHS = RHS

Here both the conditions satisfy so our answer is correct.

Hence Verified !