Question

In a rectangle the ratio of the length to the width is 2:1. Find the dimensions of the rectangle if the perimeter is 30 cm.

Answer 1

Answer:

let

l=2x

b=x

thus perimeter = 2(l+b)

              30cm = 2(2x+x)

                 15cm=3x

                   5cm=x

the length=2*5=10cm

the breadth=5cm

                         

Step-by-step explanation:

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Answer 2

Answer :-

• The dimensions of the rectangle are 10 cm and 5 cm.

Given :-

• In a rectangle, the ratio of the length to the width is 2 : 1.
• The perimeter is 30 cm.

To find :-

• The dimensions of the rectangle.

Step-by-step explanation :-

• The ratio of the length to the width is 2 : 1.
• So, let the length and width be 2x and x respectively.

• The perimeter of the rectangle is 30 cm.

We know that :-

$\underline{\boxed{\sf Perimeter \: of \: a \:rectangle = 2 \: (L + B)}}$

Here,

• Length = 2x.
• Breadth = x.

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$\underline{\underline{\mathfrak{Substituting \: these\: values \:in \:the \:formula,}}}$

$\boxed{\tt 30 = 2 \: (2x + x)}$

Adding the variable terms inside the brackets,

$\boxed{\tt30 = 2 \: (3x)}$

Removing the brackets,

$\boxed{\tt30 = 2 \times 3x}$

Multiplying 2 by 3x,

$\boxed{\tt 30 = 6x}$

Transposing 6 from RHS to LHS, changing it's sign,

$\boxed{\tt\dfrac{30}{6} = x}$

Dividing 30 by 6,

$\overline{\boxed{\tt5 \: cm = x.}}$

• The value of x is 5 cm.

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Hence, the dimensions of the rectangle are as follows :-

$\bf Length = 2x = 2 \times 5=10 \: cm.$

$\bf Breadth = x = 5 \: cm.$