Question

What is the perimeter of a rectangular whose area is 92 square mm and length is 11.5 mm​

Answer 1

• Perimeter = 39 mm

Explanation:

In this question we are given with ,

• Area of rectangle = 92 sq mm

• Length of rectangle = 11.5 mm

And we're asked to find the perimeter of rectangle .

Solution : -

We know that ,

`\pink{ \boxed{\sf{Area \: of \: rectangle = L × W}}}`

Where ,

• L = length of rectangle

• W = width of rectangle

So from this formula we can find the width of rectangle and equating it with 92 ( because 92 is the given area ) . Substituting value of length :

`\longmapsto \: 11.5 * W = 92`

Step 1 : Multiplying 11.5 and W :

`\longmapsto \: 11.5W = 92`

Step 2 : Dividing by 11.5 on both side :

`\longmapsto \: \frac{ \cancel{11.5}W}{ \cancel{ 11.5}} = (92)/(11.5)`

On further calculations we get :

`\longmapsto \: W = \cancel{(920)/(115) }`

Step 3 : By cancelling 920 by 115 we get :

`\longmapsto \: \purple{\boxed{ \bold{W = 8 \: mm}}}`

• Therefore , width of rectangle is 8 mm .

Finding Perimeter :

We know that ,

`\blue{ \boxed{ \sf{Perimeter \: of \: rectangle = 2 ( L +W )}}}`

Where ,

• L = Length of rectangle

• W = Width of rectangle

Substituting values in formula :

`\longrightarrow \: 2(11.5 + 8)`

Step 1 : Solving parenthesis :

`\longrightarrow \: 2(19.5)`

Step 2 : Multiplying 2 with 19.5 :

`\longrightarrow \: \green{\boxed{ \bold{39 \: mm}}}`

• Therefore, perimeter of rectangle is 39 mm.

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Answer 2

We are given –

• Area of rectangular is = 92 square mm
• Length of rectangular is = 11.5 mm

• We are asked to find out the value of perimeter of the rectangular! Let's find it's breadth first!

We know that–

`\qquad`
`\purple{\bf\longrightarrow Area_((Rectangular)) = Length * Breadth}`

`\qquad`
`\sf \longrightarrow 92 = 11.5 * Breadth`

`\qquad`
`\sf \longrightarrow Breadth = \cancel{(92)/(11.5)}`

`\qquad`
`\purple{\bf \longrightarrow Breadth = 8 \: mm}`

Now, Perimeter of rectangular –

`\qquad`
`\pink{\bf \longrightarrow Perimeter _((Rectangular) ) = 2( Length + Breadth) }`

`\qquad`
`\sf \longrightarrow Perimeter _((Rectangular) )= 2( 11.5 +8)`

`\qquad`
`\sf \longrightarrow Perimeter _((Rectangular) ) = 2 * 19.5`

`\qquad`
`\pink{ \bf \longrightarrow Perimeter _((Rectangular) ) = 39\: mm}`

• Henceforth, Perimeter of rectangular is 39mm.

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