Question

Length of the rectangle is 16 m less than twice is breadth if the perimiter of triangle is 82m Finds it length and breadth
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Answer 1

Correct Question:-

Length of the rectangle is 16 m less than twice is breadth if the perimiter of rectangle is 82m Finds it length and breadth.

Solution:-

Let ' a ' be the length of rectangle.

' b ' be the breadth of rectangle.

Perimeter = 82m

a = 2b - 16 ........ ( 1 )

➭ Perimeter = 2(l + b)

➭ 82 = 2(2b - 16 + b)

➭ 82 = 4b - 32 + 2b

➭ 82 = 2b - 32

➭ 82 + 32 = 2b

➭ 2b = 114

➭ b = 114/2

➭ $\boxed{\bf{\color{yellw}{ \: b \: = \: 57 \: }}}$

Now,

Substitute b value in equation ( 1 ) to find the value of ' a '

➭ a = 2b - 16

➭ a = 2(57) - 16

➭ a = 114 - 16

$\boxed{\bf{\color{yellw}{ \: a \: = \: 98 \: }}}$

Verification:-

a = 2b - 16 ........ ( 1 )

98 = 2(57) - 16

98 = 114 - 16

98 = 98

Answer 2

Given :-

• Length of the rectangle is 16 m less than twice is breadth.
• The perimiter of rectangle is 82m

Find :-

• Finds it length and breadth.

Solution :-

So we consider a be the length of rectangle.

B = The breadth of rectangle.

$Now$, According to the Question

a = 2b - 16 .....eqn .1

Considering it as the first equation.

now ,

We know the perimeter of the rectangle , which is

Perimeter = 2(l + b)

Putting the values in the above formula :-

⇒ 82 = 2(2b - 16 + b)

⇒ 82 = 4b - 32 + 2b

⇒ 82 = 2b - 32

⇒ 82 + 32 = 2b

⇒ 2b = 114

⇒ b = 114/2

⇒ B = 57 m

By substituting value in equa.. 1 we got the value of ' a '

⇒ a = 2b - 16

⇒ a = 2(57) - 16

⇒ a = 114 - 16

⇒ a = 98 m

Hence ,

The length of the rectangle ⇒ 98m

The breadth of the rectangle ⇒ 57m