Math, asked by prashant99917, 1 year ago

The length and Breadth of a rectangle are in the ratio 3:1 . If the Perimeter of rectangle is 72m, then the length of the rectangle is​

Answers

Answered by pandaXop
19

Length = 27 m

Step-by-step explanation:

Given:

  • Length and Breadth of a rectangle are in ratio 3 : 1.
  • Perimeter of rectangle is 72 m.

To Find:

  • What is the measure of length ?

Solution: Let x be the common in given ratio. Therefore,

➟ Length = 3x m

➟ Breadth = x m

As we know that

Perimeter of Rectangle = 2(Length + Breadth)

A/q

  • Perimeter is 72 m.

\implies{\rm } 72 = 2(3x + x)

\implies{\rm } 72 = 6x + 2x

\implies{\rm } 72 = 8x

\implies{\rm } 72/8 = x

\implies{\rm } 9 = x

So,

➫ Length of rectangle = 3x = 3(9) = 27 m

➫ Breadth = x = 9 m

__________________

★ Verification ★

➙ 72 = 2(18 + 9)

➙ 72 = 2(36)

➙ 72 = 72

\large\boxed{\texttt{Verified}}

Answered by Anonymous
7

\bf\huge\red{\underline{\underline{ Question : }}}

The length and breadth of a rectangle are in the ratio 3:1. If the perimeter if rectangle is 72 cm, then the length of the rectangle is..?

\bf\huge\red{\underline{\underline{ Solution : }}}

★ Given that,

  • Length and Breadth of rectangle in ratio = 3:1
  • Perimeter of rectangle = 72 cm.

★ To find,

  • Length of rectangle.

★ Let,

  • Length (l) = 3x
  • Breadth (b) = x

★ Formula used:

  • \tt\green{ Perimeter\:of\: rectangle\: = 2(l + b) }

According to the question....

\rm\:\implies 2(3x + x) = 72

\rm\:\implies 6x + 2x = 72

\rm\:\implies 8x = 72

\rm\:\implies x = \frac{72}{8}

\rm\:\implies x = 9

\bf{\boxed{ \therefore x = 9 }}

  • Substitute the value of x to get length.

\rm\:\implies 3x =  3(9) = 27

Hence, length = 27 cm & breadth = 9 cm.

★ Verification,

  • Substitute the values of length and breadth in the formula.

\rm\:\implies 2( 27 + 9)

\rm\:\implies 2(36)

\rm\:\implies 72

Hence, it was verified.

\underline{\boxed{\bf{\purple{ \therefore Length (l) = 27 cm \: ,Breadth (b) = 9 cm. }}}}\:\orange{\bigstar}

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