Question

the length of a rectangle is 3 more inches than its width. find the length and width of the rectangle with a perimeter of 54 inches

Answer 1

Perimeter of a rectangle = 2 ( l + b )

Let the width of the rectangle be w .

Then , the length of the rectangle = w + 3

Given :-

Perimeter of the rectangle = 54 inches

Length and breadth of the rectangle :-

`54= 2(w + w + 3)`

`2(w + w + 3) = 54`

`2(2w + 3) = 54`

`4w + 6 = 54`

`4w = 54 - 6`

`4w = 48`

`w = (48)/(4)`

`\color{teal}w = 12`

Which means :-

The width of this rectangle :-

`\color{orange} 12 \: \: inches`

The length of this rectangle :-

`\color{red}= 12 + 3 \\ </p><p>\color{red}= 15 \: inches`

Let us check whether we have found out the correct measurement of length and width or not by checking whether they form the given perimeter :-

`= 2(l + b) = 54`

`= 2(12 + 15) = 54`

`= 24 + 30 = 54`

`54 = 54`

LHS = RHS , which means we have found out the correct measurement of the length and width of this rectangle .

Therefore , the length of this rectangle = 15 inches and the width of this rectangle = 12 inches .