Question

The length of a rectangle is 5 more than the width what are the dimensions of the rectangle if the perimenter is 34?

Answer 1

$\huge{\underline{\bf{\pink{AnsWer \: :}}}}$

Let's say width = x

Then, length will be = (x + 5)

∴ Perimeter of a rectangle = 2(l + b)

=> 34 = 2(x + x + 5)

=> 34 = 2(2x + 5)

=> 34 = 4x + 10

=> 34 - 10 = 4x

=> 24 = 4x

=> 24/4 = x

=> 6 = x

Hence,

• Width = x = 6 units
• Length = (x + 5) = 11 units

Answer 2

❍ Let's say, that the width of the rectangle be x cm.

Given that,

❭❭ The length of a rectangle is five more than the width of the rectangle.

Therefore,

• Length of the rectangle = (x + 5) cm.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

As we know that,

$\bigstar\;{\underline{\boxed{\frak{Perimeter_{\:(rectangle)} = 2\Big(length + breadth\Big)}}}}$ ⠀⠀⠀

$\frak{we\;have}\begin{cases}\sf{\:\; \: Length = \bf{(x + 5)\;cm}}\\\sf{ \: \: \: Breadth = \bf{x \;cm}}\\\sf{ \: \: \: Perimeter = \bf{34\;cm}}\end{cases}$ ⠀⠀

⠀⠀⠀⠀

⠀⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Putting\;given\;values\;in\;formula\;:}}$⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

$:\implies\sf 34 = 2\times\bigg\{x + 5 + x \bigg\}\\\\\\:\implies\sf 34 = 2\times \bigg\{2x + 5\bigg\} \\\\\\:\implies\sf 34 = 4x + 10\\\\\\:\implies\sf 34 - 10 = 4x\\\\\\:\implies\sf 24 = 4x\\\\\\:\implies\sf 4x = 24\\\\\\:\implies\sf x = \cancel\dfrac{24}{4}\\\\\\:\implies\underline{\boxed{\frak{\purple{\pmb{x = 6}}}}}\;\bigstar$⠀

⠀⠀⠀⠀

Hence,

• Width of the rectangle, x = 6 cm.
• Length of the rectangle, (x + 5) = (6 + 5) = 11 cm.⠀

⠀⠀⠀⠀

$\therefore{\underline{\textsf{Hence, dimensions of the rectangle are \textbf{6 cm} \sf{and} \textbf{11 cm} \sf{respectively.}}}}$⠀⠀⠀⠀⠀⠀⠀⠀