Question

Question

The expressions x - 2 and x + 3 represent the length and width of a rectangle, respectively. If the area of
the rectangle is 24, what is the perimeter of the rectangle?
O 20
022
O24
O28

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Let's get it solved ~

We have been given length and width of a rectangle in terms of x ~

that is :

• length = x + 3

• width = x - 2

Area of the rectangle is given ~ i.e 24 unit²

Area of rectangle in terms of x is :

`\qquad \sf  \dashrightarrow \:(x - 2) \sdot(x + 3) = 24`

`\qquad \sf  \dashrightarrow \: {x}^(2) + 3x - 2x - 6= 24`

`\qquad \sf  \dashrightarrow \: {x}^(2) +x - 6 - 24 = 0`

`\qquad \sf  \dashrightarrow \: {x}^(2) +x -30= 0`

`\qquad \sf  \dashrightarrow \: {x}^(2) + 6x - 5x - 30 = 0`

`\qquad \sf  \dashrightarrow \: {x}^{}( x + 6) - 5(x + 6)= 0`

`f(x) = \begin{cases}x = - 6 \: \textsf{ \: if \:x + 6 = 0 } \\ \\ x = 5 \: \: \: \: \: \: \textsf{if \: x - 5 = 0} \end{cases}`

but since side of a rectangle can't be negative, we have to take value of x as 5

now, Perimeter of rectangle is ~

`\qquad \sf  \dashrightarrow \:2(width \: + \: length)`

`\qquad \sf  \dashrightarrow \:2(x - 2 + x + 3)`

`\qquad \sf  \dashrightarrow \:2(2x + 1)`

plug In the value of x ~

`\qquad \sf  \dashrightarrow \:2(2(5) + 1)`

`\qquad \sf  \dashrightarrow \:2(10 + 1)`

`\qquad \sf  \dashrightarrow \:2(11)`

`\qquad \sf  \dashrightarrow \:22 \: \: units`

So, the correct choice is b~