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The width of a rectangle is x cm. The length is 6 cm more than the width and the perimeter of the rectangle is 40 cm long.

(a) Form an equation in a and solve it to find the length of the rectangle.

(b) Hence, find the area of the rectangle.​

Sagot :

TheAmethyst

Answer:

(a)

  • Equation = 2x + 6 = 20
  • Length = 13 cm

(b)

  • Area = 91 cm²

Step-by-step explanation:

In the question we are given with ,

  • Width of rectangle = x cm

  • Length of rectangle = x + 6 cm ( Because in the question it is given that length of rectangle is 6 more than its width )

  • Perimeter of rectangle = 40 cm

And we are asked to :

  • Form an equation and find length.

  • Find Area of rectangle

(a) For finding equation and length ;

We know that ,

[tex] \red {\boxed{ \rm{Perimeter \: of \: rectangle = 2 ( L + W )}}}[/tex]

Where ,

  • L = length of rectangle
  • W = width of rectangle

Substituting value of length and breadth in formula and equating it with 40 to form the equation :

[tex] \longmapsto \: 2(x + 6 + x) = 40[/tex]

Step 1 : Solving the parenthesis :

[tex] \longmapsto \: 2(2x + 6) = 40[/tex]

Step 2 : Dividing by 2 on both side :

[tex] \longmapsto \: \frac{ \cancel{2}(2x + 6)}{ \cancel{2}} = \frac{ \cancel{40}}{ \cancel{2} }[/tex]

On further calculations we get :

[tex] \longmapsto \: \boxed{ \bold{2x + 6= 20}} - - - Equation[/tex]

Step 3 : Subtracting 6 on both sides :

[tex] \longmapsto \: 2x + 6 - 6 = 20 - 6[/tex]

On further calculations we get :

[tex] \longmapsto \: 2x = 14[/tex]

Step 4 : Dividing by 2 on both sides :

[tex] \longmapsto \: \frac{ \cancel{2}x}{ \cancel{2}} = \frac{ \cancel{14}}{ \cancel{2} }[/tex]

On further calculations we get :

[tex] \longmapsto \: \pink{ \boxed{{x = 7}}}[/tex]

We know that ,

  • x = Width of rectangle

  • x + 6 = Length of rectangle

Henceforth ,

  • Width of rectangle = 7 cm

  • Length of rectangle = 7 + 6 = 13 cm

(b) For finding area of rectangle we know that ,

[tex] \red{ \boxed{{ \rm{Area \: of \: rectangle = L \times W }}}}[/tex]

Where ,

  • L = length of rectangle
  • W = width of rectangle

Substituting value of length and breadth in the formula :

[tex] \longmapsto \: 13 \times 7[/tex]

[tex] \longmapsto \: \pink {\boxed{{91 \: cm {}^{2} }}}[/tex]

  • Therefore, area of rectangle is 91 cm² .

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