Question

The length of a rectangular field is 8m less than twice it's breadth.if the perimeter of the rectangular field is 56 meters,find its length and breadth?​

Answer 1

Given

The length of a rectangular field is 8m less than twice it's breadth.if the perimeter of the rectangular field is 56 meters.

Find out

Find the length and breadth of rectangle?

Solution

★ Let the breadth be x and length be 2x - 8

According to the given condition

• Perimeter of rectangle = 56 m

→ 2(length + breadth) = 56

→ 2[(2x - 8) + x] = 56

→ 2x - 8 + x = 56/2

→ 3x - 8 = 28

→ 3x = 28 + 8

→ 3x = 36

→ x = 36/3 = 12 m

Hence,

• Breadth of rectangle = x = 12 m
• Length of rectangle = (2x - 8) = 2*12-8 = 16m

Additional Information

• Area of rectangle = length × breath
• Perimeter of square = 4 × side
• Area of square = side × side
• Area of circle = πr²
• Perimeter of circle = 2πr

Answer 2

Answer:

$\fbox{\sf Length \ of \ rectangle = 16 \ m}$

$\fbox{\sf Breadth \ of \ rectangle = 12 \ m}$

Given:

Length of rectangle = 8 m less than twice it's breadth

Perimeter of rectangular field = 56 m

To Find:

Length and Breadth of rectangle

Step-by-step explanation:

Let the breadth of rectangle be 'b' m

So,

Length of rectangle (l) = (2b - 8) m

$\sf \implies Perimeter \: of \: rectangular \: field = 2(l + b) \\ \\ \sf \implies 56 = 2((2b - 8) + b) \\ \\ \sf \implies 56 = 2(2b - 8 + b) \\ \\ \sf \implies 56 = 2(3b - 8) \\ \\ \sf \implies 2(3b - 8) = 56 \\ \\ \sf \implies (2 \times 3b) - (2 \times 8) = 56 \\ \\ \sf \implies 6b - 16 = 56 \\ \\ \sf \implies 6b = 56 + 16 \\ \\ \sf \implies 6b = 72 \\ \\ \sf \implies b = \frac{72}{6} \\ \\ \sf \implies b = 12 \: m$

$\sf Therefore, \\ \sf Breadth \: of \: rectangle = b = 12 \: m \\ \sf Length \: of \: rectangle = (2b - 8) \: m \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 \times 12 - 8) m \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (24 - 8) m \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 16 m$