Question

The length of a rectangle is four times its width.If the perimeter is 50cm,then the length of the rectangle is​

Answer 1

D I A G R A M :

$\sf{x \:}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{4x} \\ \rm{Perimeter= 50 \: cm}$

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that the length of a rectangle is four times its width and the perimeter of the rectangle is 50 cm. We have to calculate the length of the rectangle. We'll assume the width as a variable and will error the length in the terms of width. After that, by forming a linear equation and solving that equation we'll find the value of the variable and will find the length.

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

Let,

• Width = x cm

According to the given question,

» The length of a rectangle is four times its width.

$\longmapsto$ Length = 4 × Width

$\longmapsto$ Length = 4x

As we know that,

★ Perimeter of rectangle = 2( l + w )

• l denotes length
• w denotes width

Here, perimeter = 50 cm (Given).

→ 50 = 2( 4x + x )

→ 50 = 8x + 2x

→ 50 = 10x

→ $\sf \dfrac{50}{10}$ = x

→ 5 = x

• Value of x is 5.

As per the question,

→ Length = 4x

Substituting the value of x :

→ Length = 4(5) cm

→ Length = 20 cm

Therefore, length of the rectangle is 20 cm.

More about rectangles :

• A rectangle is a quadrilateral having 4 sides, 4 angles and 4 vertices.

• Opposite sides of a rectangle are equal.

• Measure of interior angles of a rectangle is 90° each.

• Perimeter = 2(length + breadth)

• Area = Length × Breadth

Answer 2

Given :

• Length of Rectangle is 4 times than the width

• Perimeter of Rectangle is 50cm

To Find :

• Length of Rectangle

Solution :

✬ Here in the Question we are given that length of Rectangle is 4 times then the Breadth, so we will let the Breadth be y and Length be 4y. we know that Perimeter of rectangle is 2 (Length + Breadth) By putting values in the formula we can easily find the Length of the Rectangle

• Let Breadth be = y

• Let Length be = 4y

Perimeter of Rectangle = 2 (L + B)

⟼ 50 = 2 (4y + y)

⟼ 50 = 8y + 2y

⟼ 50 = 10y

⟼ y = 50/10

⟼ y = 5cm

Length of Rectangle

⟼ Length = 4y

⟼ Length = 4 × 5

⟼ Length = 20cm

∴ Length of Rectangle is 20cm