Question

The length of a rectangle is 3gm longer than a it’s width. If the perimeter of the rectangle is 34 cm what is the area

Answer 1

• 
  `{\boxed{\sf{70 \: cm^2}}}`

Explanation:

Let us consider the width of the rectangle be x cm and length be x + 3 cm

Perimeter of rectangle= 2(l +b)

`\hookrightarrow \sf 2(2x +3) = 34`

Solving for x,

`\hookrightarrow \sf 4x + 6 = 34`

Subtract 6 from both sides,

`\hookrightarrow \sf 4x + 6 - 6 = 34 -6`

`\hookrightarrow \sf 4x = 28`

Divide both sides by 4,

`\hookrightarrow \sf x = 7`

Hence,

• Length = x + 3
• length = 7 + 3
• length = 10 cm

• width = x
• width = 7 cm.

Now,

`\sf Area_((rectangle)) = length * width`

`\sf Area_((rectangle)) = 10 * 7`

`{\boxed{\sf {Area_((rectangle)) = 70 cm^2}}}`

Henceforth the area of the rectangle is 70 cm²

`\dotfill`