Question

The length of a rectangle is 6 m less than twice its breadth. If the perimeter of the rectangle is 54 find its area
Area​

Answer 1

Question:-

The length of a rectangle is 6 m less than twice its breadth. If the perimeter of the rectangle is 54 find its area

Answer:-

• The area of rectangle is 176 m².

To find:-

• Area of rectangle

Solution:-

• Perimeter of rectangle = 54 m

Let ,

• Length = 2x – 6 m
• Breadth = x m

As we know,

$\large{ \boxed{ \mathfrak{perimeter = 2(l + b)}}}$

Where,

• l = length of rectangle
• b = breadth of rectangle

According to question,

$\large{ \tt : \implies \: \: \: \: \: 2(2x - 6 + x) = 54}$

$\large{ \tt : \implies \: \: \: \: \: 3x - 6 = \frac{54}{2} }$

$\large{ \tt : \implies \: \: \: \: \: 3x = 27 + 6}$

$\large{ \tt : \implies \: \: \: \: \: 3x = 33}$

$\large{ \tt : \implies \: \: \: \: \: x = \frac{33}{3} }$

$\large{ \tt : \implies \: \: \: \: \: x = 11}$

• The value of x is 11 m

Now, we have to find the length and breadth

• Length = 2x – 6 = 2(11) – 6 = 22 – 6 = 16 m
• Breadth = x = 11 m

Thus,

• The length and breadth of rectangle are 16 m and 11 m respectively.

As we know,

$\large{ \boxed{ \mathfrak{ area = l \times b}}}$

Where,

• l = length of rectangle
• b = breadth of rectangle

According to question,

$\large{ \tt : \implies \: \: \: \: area = 11 \times 16}$

$\large{ \tt : \implies \: \: \: \: area = 176 \: {m}^{2} }$

Hence,

The area of rectangle is 176 m².