Answer:

20 and 22

Step-by-step explanation:

if we consider the length as ..x.. the. as it is said that the length and width are in consecutive even integer form the width is equal to. x+2.

so for finding length and width we will use the formula of perimeter as perimeter is given...

so the equation is.==

2(x +(x +2))=84

2(x +x +2)=84

2(2x + 2)=84

4x + 4 =84

4x = 84-4

4x=80

x=80/4

x =20

as we have considered length as x therefore length=20. and width =x+2. so 20+2=22. therefore width=22

therefore length=20 and width =22

Verified answer

Answer:

Given :-

• The length and width of a rectangle are consecutive even integers.
• The perimeter of the rectangle is 84 feet.

To Find :-

• What is the length and width of the rectangle ?

Solution :-

Let,

[tex]\small \mapsto \bf Length_{(Rectangle)} =\: a\: feet\\[/tex]

[tex]\small \mapsto \bf Width_{(Rectangle)} =\: (a + 2)\: feet\\[/tex]

Given :

• Perimeter of Rectangle = 84 feet

According to the question by using the formula we get,

[tex]\small \implies \sf\boxed{\bold{Perimeter_{(Rectangle)} =\: 2(Length + Width)}}\\[/tex]

[tex]\implies \sf 84 =\: 2\bigg\{a + (a + 2)\bigg\}\\[/tex]

[tex]\implies \sf 84 =\: 2\bigg\{2a + 2\bigg\}\\[/tex]

[tex]\implies \sf 84 =\: 4a + 4\\[/tex]

[tex]\implies \sf 84 - 4 =\: 4a\\[/tex]

[tex]\implies \sf 80 =\: 4a\\[/tex]

[tex]\implies \sf \dfrac{80}{4} =\: a\\[/tex]

[tex]\implies \sf 20 =\: a\\[/tex]

[tex]\implies \sf\bold{a =\: 20}\\[/tex]

Hence, the length and width of the rectangle will be :

[tex]\dag[/tex] Length Of Rectangle :

[tex]\leadsto \sf Length_{(Rectangle)} =\: a\: feet\\[/tex]

[tex]\leadsto \sf\bold{\underline{Length_{(Rectangle)} =\: 20\: feet}}\\[/tex]

[tex]\dag[/tex] Width Of Rectangle :

[tex]\leadsto \sf Width_{(Rectangle)} =\: (a + 2)\: feet\\[/tex]

[tex]\leadsto \sf Width_{(Rectangle)} =\: (20 + 2)\: feet\\[/tex]

[tex]\leadsto \sf\bold{\underline{Width_{(Rectangle)} =\: 22\: feet}}\\[/tex]

[tex]\therefore[/tex] The length and width of the rectangle is 20 feet and 22 feet respectively.