Math, asked by anuragawadhiya123, 9 days ago

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​

Answers

Answered by EliteZeal
58

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

 \:\:

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

 \:\:

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

 \:\:

  • Area of the hall is 450 sq. m

 \:\:

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

 \:\:

  • Difference between its length and breadth

 \:\:

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

 \:\:

  • Let the length be "x"

  • Let the width be "y"

 \:\:

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

 \:\:

➠ Length × Breadth ------- (1)

 \:\:

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

 \:\:

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

 \:\:

So,

 \:\:

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

 \:\:

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

 \:\:

  • Length = x

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

 \:\:

Putting these values in (1)

 \:\:

➠ Length × Breadth

 \:\:

➜ x ×  \sf \dfrac { x } { 2 }

 \:\:

➜ x ×  \sf \dfrac { x } { 2 } = 450

 \:\:

➜ x² = 450 × 2

 \:\:

➜ x² = 900

 \:\:

 \sf x = \sqrt {900 }

 \:\:

x = -30

➨ x = 30 ------- (3)

 \:\:

Length can't be negative , hence x = 30

 \:\:

  • Hence length of rectangular hall is 30 m

 \:\:

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

 \:\:

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

 \:\:

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

 \:\:

➨ y = 15

 \:\:

  • Hence width of rectangular hall is 15 m

 \:\:

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

 \:\:

➠ x - y

 \:\:

➜ 30 - 15

 \:\:

➨ 15

 \:\:

∴ The difference between its length and breadth is 15 m

Answered by AnkitaSahni
3

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.

Similar questions