Question

The length of a rectangle is 5 m less than three times the width . If the perimeter is 86 m. Calculate the dimensions of the rectangle

Answer 1

✬ Length = 31 m ✬

✬ Width = 12 m ✬

Step-by-step explanation:

Given:

• Length of rectangle is 5 m less than 3 times the width.
• Perimeter of rectangle is 86 m.

To Find:

• What is the length & width of rectangle?

Solution: Let the width of rectangle be x m. Therefore,

➬ Length of rectangle = 5 m less than 3 times of width.

➬ Length = (3x – 5) m

As we know that

★ Perimeter of Rectangle = 2(Length + Width)★

A/q

• Perimeter = 86 m

$\implies{\rm }$ 86 = 2(Length + Width)

$\implies{\rm }$ 86 = 2(3x – 5 + x)

$\implies{\rm }$ 86 = 2(4x – 5)

$\implies{\rm }$ 86 = 8x – 10

$\implies{\rm }$ 86 + 10 = 8x

$\implies{\rm }$ 96 = 8x

$\implies{\rm }$ 96/8 = x

$\implies{\rm }$ 12 = x

So,

➽ Width of rectangle is x = 12 cm

➽ Length of rectangle = (3x – 5) m

=> 3(12) – 5

=> 36 – 5 = 31 m

______________________

★ Verification ★

➛ 86 = 2 ( Length + Width )

➛ 86 = 2 ( 31 + 12 )

➛ 86 = 2(43)

➛ 86 = 86

$\large\boxed{\texttt{Verified}}$

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• Length of a rectangle is 5 m less than three times the width.

$\:\:$

• Perimeter is 86 m.

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The dimensions of the rectangle

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the width of rectangle be 'w' m.

$\:\:$

Length of rectangle is 5 m less than 3 times of width.

$\:\:$

$\underline{\bold{\texttt{Length :}}}$

$\:\:$

(3x – 5) m

$\:\:$

$\underline{\bold{\texttt{We know that :}}}$

$\:\:$

Perimeter of Rectangle = 2(Length + Width)

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

Perimeter = 86 m

$\:\:$

$\longmapsto \sf 86 = 2(Length + Width)$

$\:\:$

86 = 2(3x – 5 + x)

$\:\:$

86 = 2(4x – 5)

$\:\:$

86 = 8x – 10

$\:\:$

86 + 10 = 8x

$\:\:$

96 = 8x

$\:\:$

$\sf \dfrac {96 } { 8 } = x$

$\:\:$

$\bf \dashrightarrow x = 12$

$\:\:$

So,

$\:\:$

$\underline{\bold{\texttt{Width of rectangle :}}}$

$\:\:$

x = 12 cm

$\:\:$

$\underline{\bold{\texttt{Length of rectangle :}}}$

$\:\:$

(3x – 5) m

$\:\:$

3(12) – 5

$\:\:$

36 – 5

$\:\:$

$\rm \implies 31$

$\:\:$

Hence length is 31 m and width is 12 m

$\rule{200}5$