Verified answer

Answer:

• [tex]\boldsymbol x[/tex] = 5 units

Explanation:

Given,

In a rectangle the length is [tex](\boldsymbol x + 5)[/tex] units and it's breadth is [tex](\boldsymbol x + 1)[/tex] units

Find the value of [tex]\boldsymbol x[/tex] if the perimeter is 32 units.

We know that,

Perimeter of a rectangle = [tex]2(l + b)[/tex]

Where,

• [tex]l[/tex] denotes the length
• [tex]b[/tex] is the breadth of the rectangle.

[tex] \therefore \boldsymbol{ 32 = 2[(x + 5) + (x + 1) ]}[/tex]

Solving for [tex]\boldsymbol x[/tex]

[tex] \implies 32 = 2[(x + 5) + (x + 1) ][/tex]

[tex] \implies \dfrac{32}{2} = [x + 5 + x + 1][/tex]

[tex] \implies 16 = [2x + 6][/tex]

[tex] \implies 16 - 6= 2x [/tex]

[tex] \implies 10= 2x [/tex]

[tex]\therefore \boldsymbol {x = 5}[/tex]

Answer:

Given :-

• A rectangle has a length given (x + 5) units.
• The width of the rectangle is given by (x + 1) units.
• The perimeter of the rectangle is 32 units.

To Find :-

• What is the value of x.

Formula Used :-

[tex]\clubsuit[/tex] Perimeter Of Rectangle Formula :

[tex]\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar\\[/tex]

Solution :-

Given :

• Length = (x + 5) units
• Breadth = (x + 1) units
• Perimeter of the rectangle = 32 units

According to the question by using the formula we get,

[tex]\footnotesize \implies \bf Perimeter_{(Rectangle)} =\: 2(Length + Breadth)\\[/tex]

[tex]\implies \sf 32 =\: 2\{(x + 5) + (x + 1)\}\\[/tex]

[tex]\implies \sf 32 =\: 2(x + 5 + x + 1)\\[/tex]

[tex]\implies \sf 32 =\: 2(x + x + 5 + 1)\\[/tex]

[tex]\implies \sf 32 =\: 2(2x + 6)[/tex]

[tex]\implies \sf 32 =\: 4x + 12[/tex]

[tex]\implies \sf 32 - 12 =\: 4x[/tex]

[tex]\implies \sf 20 =\: 4x[/tex]

[tex]\implies \sf \dfrac{\cancel{20}}{\cancel{4}} =\: x[/tex]

[tex]\implies \sf \dfrac{5}{1} =\: x[/tex]

[tex]\implies \sf 5 =\: x[/tex]

[tex]\implies \sf\bold{\red{x =\: 5\: units}}\\[/tex]

[tex]\therefore[/tex] The value of x is 5 units .