Question

The length of a rectangle is 2 yards less than 3 times the width. The perimeter is 68 yards. Find the length and the width.

Answer 1

Question:-

The length of a rectangle is 2 yards less than 3 times the width. The perimeter is 68 yards. Find the length and the width.9

Answer:-

• The sides of rectangle are 25 yards and 9 yards.

Solution:-

• Length = 3x - 2 yards
• Breadth = x yards
• Perimeter = 68 yards

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

$\large{ : \implies \: 2(3x - 2 + x) = 68}$

$\large{ : \implies \: 4x - 2 = \frac{68}{2} }$

$\large{ : \implies \: 4x = 34 + 2}$

$\large{ : \implies \: 4x = 36}$

$\large{ : \implies \: x = \frac{36}{4} }$

$\large{ : \implies \: x = 9 \: yards}$

• The value of x is 9 yards.

_________________________

• Length = 3x - 2 = 3(9) - 2 = 25 yards
• Breadth = x = 9 yards

_________________________

The sides of rectangle are 25 yards and 9 yards.

Answer 2

Answer :-

• Dimensions of the rectangle are 9 yards and 25 yards respectively.

Given :-

• The length of a rectangle is 2 yards less than 3 times the width. The perimeter is 68 yards.

To Find :-

• Length and width of the rectangle.

Solution :-

Let

• Breadth of the rectangle be x
• Length of the rectangle will be 3x - 2

Given

• The perimeter of the rectangle is 68yards.

As we know that

• Perimeter of the rectangle is 2 (l + b)

Where

• l = length
• b = breadth

According to question :-

⇒ 2 {(3x - 2) + x} = 68

⇒ 2 { 3x - 2 + x } = 68

⇒ 2 { 3x + x - 2 } = 68

⇒ 2 { 4x - 2 } = 68

⇒ 4x - 2 = 68/2

⇒ 4x - 2 = 34

⇒ 4x = 34 + 2

⇒ 4x = 36

⇒ x = 36/4

⇒ x = 9

Now

• Breadth of the rectangle = x = 9 yards
• Length of the rectangle = 3x - 2 = 3(9) - 2 = 25 yards

Hence, the dimensions of the rectangle are 9 yards and 25 yards respectively.