Answer:
(a)
- Equation = 2x + 6 = 20
- Length = 13 cm
(b)
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.
(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 + 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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