Question

❗️❗️❗️❗️PLS ❗️❗️The area of a rectangle is 35. If the length is 2 more than the width, find the dimensions of the rectangle. [Only an algebraic solution!!!!]​

Answer 1

Given

• Area of rectangle = 35
• Length = x+2
• Width = x

To find

• Dimensions of the rectangle = ?

Solution

• 
  `\sf \purple \dashrightarrow \orange{area = length * width}`
• 
  `\sf \purple \dashrightarrow \orange{35= (x+2)* x}`
• 
  `\sf \purple \dashrightarrow \orange{35 = {x}^(2) + 2x}`
• 
  `\sf \purple \dashrightarrow \orange{35 - {x}^(2) - 2x = 0}`
• 
  `\sf \purple \dashrightarrow \orange{ - 35 + {x}^(2) + 2x = 0}`
• 
  `\sf \purple \dashrightarrow \orange{ {x}^(2) + 2x - 35 = 0 }`
• 
  `\sf \purple \dashrightarrow \orange{ {x}^(2) + 7x - 5x - 35 = 0 }`
• 
  `\sf \purple \dashrightarrow \orange{ x * (x + 7) - 5(x + 7) = 0 }`
• 
  `\sf \purple \dashrightarrow \orange{ x = - 7, x = 5 }`

Since, The dimension cannot be in negative we will consider the value of x as 5...

Now,

`\tt \pink \multimap \blue{length = x + 2 = > 5 + 2 = > 7}`

`\tt \pink \multimap \blue{width = x = > 5}`

Answer 2

Given :

• The area of a rectangle is 35. If the length is 2 more than the width.

To Find :

• The dimensions of the rectangle.

Solution :

• Let's assume the width of the rectangle as " x "
• As, the length is 2 more than the width, So the Length will be "(x + 2)"

We know that,

• 
  `\bf{ Length * width = Area }`

So, Substituting the given values :

`\qquad \sf \: { \dashrightarrow (x + 2) * x = 35}`

`\qquad \sf \: { \dashrightarrow {x}^(2) + 2x = 35}`

`\qquad \sf \: { \dashrightarrow {x}^(2) + 2x - 35 = 0}`

`\qquad \sf \: { \dashrightarrow {x}^(2) + 7x + 5x - 35 = 0}`

`\qquad \sf \: { \dashrightarrow {x}(x + 7) - 5(x + 7) = 0}`

`\qquad \sf \: { \dashrightarrow ({x}- 5)(x + 7) = 0}`

`\qquad \sf \: { \dashrightarrow \: x =5 , x = - 7}`

Note :

• The width can't be a negative number, so we can't choose x = -7, So we need to choose x = 5

Hence ,

• Width = 5
• Length = 5 + 2 = 7

Therefore ,

• The dimensions of the rectangle are 5 and 7