Question

9. The width of a rectangular hall is 1/2 of its length. If the area of the hall is 450 sq.m, what is the
difference between its length and breadth?n​

Answer 1

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

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

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• Width of a rectangular hall is 1/2 of its length

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• Area of the hall is 450 sq. m

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

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• Difference between its length and breadth

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

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• Let the length be "x"

• Let the width be "y"

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$\underline{\bold{\texttt{Area of rectangle :}}}$

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➠ Length × Breadth ------- (1)

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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Width of a rectangular hall is 1/2 of its length

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So,

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➠ $\sf y = \dfrac { 1 } { 2 } \times x$ --- (2)

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$\underline{\bold{\texttt{Area of rectangular hall :}}}$

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• Length = x

• Width = y = $\sf \dfrac { x } { 2 }$

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Putting these values in (1)

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➠ Length × Breadth

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➜ x × $\sf \dfrac { x } { 2 }$

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➜ x × $\sf \dfrac { x } { 2 } = 450$

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➜ x² = 450 × 2

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➜ x² = 900

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➜ $\sf x = \sqrt {900 }$

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x = -30

➨ x = 30 ------- (3)

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Length can't be negative , hence x = 30

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• Hence length of rectangular hall is 30 m

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$\underline{\bold{\texttt{Putting x = 30 from (3) to (2) }}}$

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➜ $\sf y = \dfrac { 1 } { 2 } \times x$

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➜ $\sf y = \dfrac { 1 } { \cancel 2 } \times \cancel 30$

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➨ y = 15

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• Hence width of rectangular hall is 15 m

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Now we need to find the difference between its length and breadth

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➠ x - y

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➜ 30 - 15

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➨ 15

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∴ The difference between its length and breadth is 15 m

Answer 2

Given:

The width of a rectangular hall is 1/2 of its length.

Area of the hall = 450 m²

To Find:

Difference between the hall's length and breadth

Solution:

• What is the area of a rectangle?

               The Area of a rectangle is given by:

                   A = length × breadth

• As per the given question,

              Let the length of the rectangular hall be x m

              Then the width of the hall will be $\frac{x}{2}$ m

• Now we put these variables into the formula for area:

                        (x). ($\frac{x}{2}$) = 450

                          ⇒ $\frac{x^{2} }{2}$ = 450

                          ⇒ x² = 900

                         ⇒  x = √900 = 30

Therefore, length of the hall = 30 m

And the width of the hall = $\frac{30}{2}$ = 15 m

Hence, difference between length and width

                      = 30 -15

                      = 15 m

Therefore, the difference between its length and breadth is 15 m.