Question

The perimeter of a rectangle is 85 feet. The length of the rectangle is 2( x + 16 ) and the width is 3x-1. What is the length of the rectangle?

Answer 1

Given :-

• Perimeter of rectangle = 85 feet
• Length = 2(x + 16)
• Width = 3x - 1

To find :-

• Length of rectangle = ?

Solution :-

As we know,

Perimeter of rectangle = 2(length + breadth)

• For finding the length of rectangle. Firstly, find the value of x by using the formula of perimeter of rectangle.

$\mapsto$ 85 = 2[2(x + 16) + 3x - 1]

$\mapsto$ 85 = 2[2x + 32 + 3x - 1]

$\mapsto$ 85 = 2[5x + 31]

$\mapsto$ 85 = 10x + 62

$\mapsto$ 85 - 62 = 10x

$\mapsto$ 23 = 10x

$\mapsto$ $\sf{x~=~\dfrac{23}{10}}$

$\mapsto$ x = 2.3

• The value of x is 2.3

Length of rectangle = 2(x + 16) = 2(2.3 + 16) = 36.6 feet.

_____________________

Some related formulae :-

• Area of rectangle = length × breadth
• Diagonal = $\sf\sqrt{w^2 + l^2}$

Answer 2

Given :-

• Perimeter of rectangle = 85 feet

• Length = 2(x + 16)

• Width = 3x - 1

To find :-

• Length of rectangle = ?

Solution :-

As we know,

$\boxed{\bold{Perimeter~of~rectangle~= 2(length + breadth)}}$

↦ 85 = 2[2(x + 16) + 3x - 1]

↦ 85 = 2[2x + 32 + 3x - 1]

↦ 85 = 2[5x + 31]

↦ 85 = 10x + 62

↦ 85 - 62 = 10x

↦ 23 = 10x

↦ $\sf{x~=~\dfrac{23}{10}}$

↦ x = 2.3

The value of x is 2.3

• Length of rectangle = 2(x + 16) = 2(2.3 + 16) = 36.6 feet.