Question

The length of a rectangleular field in 8meters less than twice it's breadth.if the perimeter of the rectangleular field is 56 meters, find it's length and bredth​

Answer 1

Given :-

• Length is 8 metre less than twice of Breadth
• Perimeter of the rectangle is 56 metres

Let the Breadth be x

Therefore, length = 2x - 8

So,putting the values, we get,

$\sf = > 2(x + 2x - 8) = 56 \: m \\ \sf \: = > 6x - 16 = 56 \: m \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \: = > 6x = 56 + 16 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > \sf \: x = \frac{72}{6} = 12 \: m \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the length of the field

=> 2x - 8

=> 24 - 8

=> 16 m

And the width = x = 12m

Hope it helps you mate! :)

Answer 2

Answer

• Length = 16 meter.
• Breadth = 12 meter.

Given

• The length of a rectangular field is 8 meter less than twice it's breadth.

• Perimeter of rectangle = 56 meters.

To Find

• The length and breadth of the rectangle.

Step By Step Explanation

Assumption :

Let us assume that the breadth of the rectangular field = x. Then length will be 2x - 8.

Formula Used :

$\underline{ \boxed{ \bold{ \purple{Perimeter_{(Rectangle)} = 2(Length + Breadth)}}}} \: \: \: \: \: \red \bigstar$

By substituting the values :

$\longmapsto \sf2(2x - 8 + x) = 56 \\ \\ \longmapsto \sf2(3x - 8) = 56 \\ \\ \longmapsto \sf3x - 8 = \cancel \cfrac{56}{2} \\ \\\longmapsto \sf 3x - 8 = 28 \\ \\\longmapsto \sf 3x = 28 + 8 \\ \\\longmapsto \sf 3x = 36 \\ \\\longmapsto \sf x = \cancel \cfrac{36}{3} \\ \\\longmapsto \underline {\boxed{\bold{ \green{ x = 12 \: meter}}}}\:\:\:\:\red\bigstar$

Therefore, length = 2x - 8 => 24 - 8 → 16 meter and breadth = 12 meter.

_____________________________