Question

Length of a rectangle is 8m less than twice it's breadth. The perimeter of the rectangle is 56m. Find it's length and breadth? ​

Answer 1

Step-by-step explanation:

Let the breadth of the rectangle be x m. Then,

length of the rectangle =(2x−8) m

Given, perimeter =56 m

⟹2(2x−8+x)=56

⟹2(3x−8)=56

⟹6x−16=56

⟹6x=56+16[Transposing−16toRHS]

⟹6x=72

⟹x=12

Therefore, breadth of the rectangle =12 m and length of the rectangle =2×12−8=16 m

Answer 2

Answer:

• Length of rectangle is 16 m.
• Breadth of rectangle is 12 m.

Step-by-step explanation:

To find:-

• Length and breadth.

Solution:-

Given that,

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

Perimeter of rectangle is 56 m.

Let, Breadth of rectangle be x.

And, Length be rectangle be 2x - 8 [We take 2x - 8 to be breadth because it is given 8 m is less than twice the breadth.

Perimeter of rectangle = 2(l + b)

• Where, l and b are length and breadth of rectangle.

Putting the values in formula :

$\longrightarrow$ 56 = 2[(2x - 8) + x]

$\longrightarrow$ 56 = 2(2x - 8 + x)

$\longrightarrow$ 56 = 4x - 16 + 2x

$\longrightarrow$ 56 = 6x - 16

$\longrightarrow$ 56 + 16 = 6x

$\longrightarrow$ 72 = 6x

$\longrightarrow$ 72/6 = x

$\longrightarrow$ 12 = x

Or, $\longrightarrow$ x = 12

Verification:-

$\longrightarrow$ 56 = 2[(2x - 8) + x]

• Put x = 12

$\longrightarrow$ 56 = 2[(2×12 - 8) + 12]

$\longrightarrow$ 56 = 2(16 + 12)

$\longrightarrow$ 56 = 32 + 24

$\longrightarrow$ 56 = 56

Hence, Verified!!

We have taken, Breadth be x. So, Breadth of rectangle is 12 m.

We have also taken Length be 2x - 8 = 2×12 - 8 = 24 - 8 = 16. Thus, Length of rectangle is 16 m.